Introduction

Self-assessed health is a widely used indicator to gauge the well-being in polulation setting. Identifying aspects linked to individuals’ self-assessments of their health may help to prioritize factors that can be addressed in advance, thus, shifting focus from treating illnesses to preventing them (Clark, Cheryl R., et al., 2021).

Our study explores the predictors of decline of self-assessed health and worries about health. We investigate the connection between self-asessed health decline and demographic, socio-economic and other health-related factors using Lasso Regression and Random Forest and how these factors compare to the predictors of health-related worries.

We exploit the data retrieved from German Socioeconomic Panel (G-SOEP) – a longitudinal household survey that has been conducted in Germany annually since 1984, which collects detailed data from individuals and households. Our dataset includes subjective health measures (self-assessed health, worries about health and health satisfaction), health-related factors, labour market variables and socio-demographic characteristics. We restrict the analysis to individuals aged between 25 and 55 years old. Due to absence of essential variables before 2001 our panel contains data since 1999 up to the last available year - 2019.

1. Setup

1.1 Load Required Packages

# Load required packages
my_packages <- c("tidyverse", "haven", "openxlsx", "labelled", "dplyr", "lubridate","ggplot2","skimr","ggcorrplot","patchwork","ggridges", "glmnet", "plm", "magrittr", "caret","waffle","randomForest","rpart","ranger","vip","pdp","rpart.plot","fastDummies","ROSE")

for (p in my_packages) {
  if (!require(p, character.only = TRUE)) {
    install.packages(p, dependencies = TRUE)
  }
  library(p, character.only = TRUE)
}

## Loading required package: tidyverse

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1.2 Load the pl Dataset

main <- read_dta('/Users/salmahoumane/Documents/R/pl.dta') %>%
  select(
    "pid", "syear", "ple0008", "plh0035", "ple0055", "ple0056", "ple0072", "ple0081_h", "ple0086_v4",
    "ple0080_v2", "ple0086_v1", "ple0086_v4", paste0("ple00", 11:23),
    "ple0004", "ple0005", "ple0095", "plh0182", "plh0171",
    "plh0042", "plh0033", "plh0032", "ple0010_h", "ple0006", "ple0007"
  )
cat("Main dataset dimensions:", dim(main), "\n")

## Main dataset dimensions: 377869 35

1.3 Merge with Other Datasets

# Merge with `pgen` dataset
data_pgen <- read_dta('/Users/salmahoumane/Documents/R/pgen.dta') %>%
  select("pid", "syear", "pgerwzeit", "pgemplst", "pglabnet", "pgtatzeit", "pgexpue", "pgstib","pgfamstd", "pgisced11")
cat("PGEN dataset dimensions:", dim(data_pgen), "\n")

## PGEN dataset dimensions: 381814 10

main_before_merge <- dim(main)  # Store dimensions before merge
main <- merge(main, data_pgen, by = c("pid", "syear"), all.x = TRUE)
cat("After merging with pgen: Rows =", nrow(main), "Cols =", ncol(main), "\n")

## After merging with pgen: Rows = 377869 Cols = 43

cat("Same number of rows then the main dataset with 7 new rows -> Merge successful")

## Same number of rows then the main dataset with 7 new rows -> Merge successful

# Check for duplicate rows introduced during merge
duplicates <- main %>%
  group_by(pid, syear) %>%
  summarise(count = n()) %>%
  filter(count > 1)

## `summarise()` has grouped output by 'pid'. You can override using the `.groups`
## argument.

if (nrow(duplicates) > 0) {
  cat("Warning: Duplicates detected after merging with pgen!\n")
  print(duplicates)
} else {
  cat("No duplicates found after merging with pgen.\n")
}

## No duplicates found after merging with pgen.

# Merge with `ppathl` dataset
data_ppathl <- read_dta('/Users/salmahoumane/Documents/R/ppathl.dta') %>%
  select("pid", "hid", "syear", "psample", "gebjahr", "sex", "migback", "germborn")
cat("PPATHL dataset dimensions:", dim(data_ppathl), "\n")

## PPATHL dataset dimensions: 634864 8

main_before_ppathl <- dim(main)  # Store dimensions before second merge

main <- left_join(main, data_ppathl, by = c("pid", "syear"))
cat("After merging with ppathl: Rows =", nrow(main), "Cols =", ncol(main), "\n")

## After merging with ppathl: Rows = 377869 Cols = 49

cat("Same number of rows then the main dataset with 6 new rows -> Merge successful")

## Same number of rows then the main dataset with 6 new rows -> Merge successful

# Final snapshot of dimensions
cat("Final dataset dimensions after all merges:", dim(main), "\n")

## Final dataset dimensions after all merges: 377869 49

1.4 Main filtering: Analysis post 1999

We remove all years before 1999 as the dataset does not contain informtion on health related worries before 1999.

# Drop observations prior to 1999
main <- main %>%
  filter(syear >= 1999)
cat("Dimensions:", dim(main), "\n")

## Dimensions: 287810 49

2. Outcome Variables: Subjective Health

2.1 Health

# Clean and rename the `health` variable
main <- main %>%
  rename(health = ple0008) %>%
  filter(health != -1) %>%  # Filter those who refused to answer -> 398 observations dropped
    mutate(health = case_when(health == 5 ~ 1, # Reverse the scale: 1 -> 5, 5 -> 1
                            health == 4 ~ 2,
                            health == 3 ~3,
                            health == 2 ~ 4,
                            health == 1 ~ 5))

sum(is.na(main$health))  # no missings

## [1] 0

# Visualisation: Bar plot
ggplot(main, aes(x = factor(health))) +
  geom_bar(fill = "steelblue") +
  labs(
    title = "Distribution of Self-Assessed Health",
    x = "Health Category (1 = Poor, 5 = Excellent)",
    y = "Count"
  ) +
  theme_minimal()

#Visualisation: Line plot
# Line plot: Average health over years
main %>%
  group_by(syear) %>%
  summarize(avg_health = mean(health, na.rm = TRUE)) %>%
  ggplot(aes(x = syear, y = avg_health)) +
  geom_line(color = "darkgreen") +
  geom_point(color = "darkgreen") +
  labs(
    title = "Average Self-Assessed Health Over Years",
    x = "Survey Year",
    y = "Average Health"
  ) +
  theme_minimal()

2.2 Worries About Health

# Create `worr_health_categorical` and `worr_health_dummy`
main <- main %>%
  rename(worr_health_categorical = plh0035) %>%
  filter(worr_health_categorical != -1 & worr_health_categorical!= -4) %>% # drop those who refused to answer -> 1287 obs
  mutate(
    worr_health_categorical = case_when(
      worr_health_categorical < 0 ~ NA_real_,
      TRUE ~ worr_health_categorical
    )
  ) %>%
  group_by(pid) %>%
  mutate(
    worr_health_categorical = if_else(
      syear %in% c(2011, 2012, 2013) & is.na(worr_health_categorical), #impute the years 2011-2013 because 11000 observations werent asked this question in these years
      floor(
        mean(
          worr_health_categorical[syear %in% c(2010, 2014)],
          na.rm = TRUE
        )
      ),
      worr_health_categorical
    )
  ) %>%
  ungroup() %>%
  drop_na(worr_health_categorical) %>% # drop those who had too little information to be reasonably imputed-> 1032 obs
  mutate(worr_health_categorical = case_when(
                            worr_health_categorical == 3 ~ 1, # Reverse the scale: 1 = no worries
                            worr_health_categorical == 2 ~ 2,
                            worr_health_categorical == 1 ~ 3), # 3 = lots of worries
    worr_health_dummy = if_else(
      worr_health_categorical >= 2, 1, 0
    )
  )

# Visualisation: Bar plot (categorical)
ggplot(main, aes(x = worr_health_categorical)) +
  geom_bar(fill = "coral") +
  labs(
    title = "Distribution of Worries About Health",
    x = "Worries About Health (1 = no worries; 3 = large worries)",
    y = "Count"
  ) +
  theme_minimal()

# Visualisation: Pie Char (dummy)
main %>%
  group_by(worr_health_dummy) %>%
  summarize(count = n()) %>%
  mutate(
    proportion = count / sum(count),
    label = paste0(round(proportion * 100, 1), "%")
  ) %>%
  ggplot(aes(x = "", y = proportion, fill = factor(worr_health_dummy))) +
  geom_bar(stat = "identity", width = 1) +
  coord_polar("y") +
  labs(
    title = "Proportion of Health Worry (Dummy)",
    fill = "Health Worry (Dummy)"
  ) +
  theme_minimal() +
  geom_text(aes(label = label), position = position_stack(vjust = 0.5))

2.3 Health Trends

# Create health decline dummy for 2 years into the future
main <- main %>%
  arrange(pid, syear) %>%  # Sort data by pid and syear
  group_by(pid) %>%
  mutate(
    health_in_2yrs = dplyr::lead(health, n = 2, order_by = syear),
    health_decline_2yrs = case_when(
      !is.na(health_in_2yrs) & health_in_2yrs < health ~ 1,  # Decline
      !is.na(health_in_2yrs) & health_in_2yrs >= health ~ 0,  # No decline
      TRUE ~ NA_real_  # NA for missing data
    )
  ) %>%
  ungroup()

# Check for missing values in health_in_2yrs
sum(is.na(main$health_in_2yrs))  # 81.113

## [1] 81113

  # we are not yet dropping those observations because tey might be useful for the imputation of other variables

3. Predictors

3.2 Life Satisfaction and Health Satisfaction

# Create life_satisfaction and health_satisfaction variables
# Track Missing Categories Before Imputation
missing_breakdown_before <- main %>%
  summarise(
    plh0182_NA = sum(is.na(plh0182)),
    plh0182_not_asked = sum(plh0182 %in% c(-8, -5), na.rm = TRUE),
    plh0182_other_neg = sum(plh0182 < 0 & !(plh0182 %in% c(-8, -5)), na.rm = TRUE),
    plh0171_NA = sum(is.na(plh0171)),
    plh0171_not_asked = sum(plh0171 %in% c(-8, -5), na.rm = TRUE),
    plh0171_other_neg = sum(plh0171 < 0 & !(plh0171 %in% c(-8, -5)), na.rm = TRUE)
  )

print("Breakdown of missing values before imputation:")

## [1] "Breakdown of missing values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 6
##   plh0182_NA plh0182_not_asked plh0182_other_neg plh0171_NA plh0171_not_asked
##        <int>             <int>             <int>      <int>             <int>
## 1          0              1840               519          0              2862
## # ℹ 1 more variable: plh0171_other_neg <int>

# Drop those who refused to answer or answered invalidly
main <- main %>%
  filter(!(plh0182 %in% c(-1, -2, -3) | plh0171 %in% c(-1, -2, -3))) # 908 observations

# Impute remaining Values for plh0182 and plh0171 with Max 2-Year Lag/Lead
main <- main %>%
  arrange(pid, syear) %>%  
  group_by(pid) %>%
  mutate(
    # Flag rows that will be imputed
    imputed_flag_life = if_else(plh0182 %in% c(-5, -8) | is.na(plh0182), 1, 0),
    imputed_flag_health = if_else(plh0171 %in% c(-5, -8) | is.na(plh0171), 1, 0),

    # Replace -5 and -8 with NA
    plh0182 = case_when(plh0182 %in% c(-5, -8) ~ NA_real_, TRUE ~ plh0182),
    plh0171 = case_when(plh0171 %in% c(-5, -8) ~ NA_real_, TRUE ~ plh0171),

    # Impute plh0182 (life satisfaction)
    life_satisfaction = if_else(
      is.na(plh0182),
      coalesce(
        if_else(syear - lag(syear) <= 2 & !is.na(lag(plh0182)), lag(plh0182), NA_real_),
        if_else(dplyr::lead(syear) - syear <= 2 & !is.na(dplyr::lead(plh0182)), dplyr::lead(plh0182), NA_real_)
      ),
      plh0182
    ),

    # Impute plh0171 (health satisfaction)
    health_satisfaction = if_else(
      is.na(plh0171),
      coalesce(
        if_else(syear - lag(syear) <= 2 & !is.na(lag(plh0171)), lag(plh0171), NA_real_),
        if_else(dplyr::lead(syear) - syear <= 2 & !is.na(dplyr::lead(plh0171)), dplyr::lead(plh0171), NA_real_)
      ),
      plh0171
    )
  ) %>%
  ungroup()

# Breakdown After Imputation
missing_breakdown_after <- main %>%
  summarise(
    life_satisfaction_NA = sum(is.na(life_satisfaction)),
    health_satisfaction_NA = sum(is.na(health_satisfaction))
  )

print("Breakdown of missing values after imputation:")

## [1] "Breakdown of missing values after imputation:"

print(missing_breakdown_after)

## # A tibble: 1 × 2
##   life_satisfaction_NA health_satisfaction_NA
##                  <int>                  <int>
## 1                  328                    681

# Drop observations that are still missing
main <- main %>%
  filter(!is.na(life_satisfaction) & !is.na(health_satisfaction)) # 681 observations dropped

# Step 4: Descriptive Statistics
# Imputed Rows
imputed_stats <- main %>%
  filter(imputed_flag_life == 1 | imputed_flag_health == 1) %>%
  summarise(
    Life_Satisfaction_Mean = mean(life_satisfaction, na.rm = TRUE),
    Life_Satisfaction_Median = median(life_satisfaction, na.rm = TRUE),
    Health_Satisfaction_Mean = mean(health_satisfaction, na.rm = TRUE),
    Health_Satisfaction_Median = median(health_satisfaction, na.rm = TRUE),
    Count = n()
  )

# Non-Imputed Rows
non_imputed_stats <- main %>%
  filter(imputed_flag_life == 0 & imputed_flag_health == 0) %>%
  summarise(
    Life_Satisfaction_Mean = mean(life_satisfaction, na.rm = TRUE),
    Life_Satisfaction_Median = median(life_satisfaction, na.rm = TRUE),
    Health_Satisfaction_Mean = mean(health_satisfaction, na.rm = TRUE),
    Health_Satisfaction_Median = median(health_satisfaction, na.rm = TRUE),
    Count = n()
  )

print("Descriptive Statistics for Imputed Rows:")

## [1] "Descriptive Statistics for Imputed Rows:"

print(imputed_stats)

## # A tibble: 1 × 5
##   Life_Satisfaction_Mean Life_Satisfaction_Median Health_Satisfaction_Mean
##                    <dbl>                    <dbl>                    <dbl>
## 1                   7.53                        8                     7.06
## # ℹ 2 more variables: Health_Satisfaction_Median <dbl>, Count <int>

print("Descriptive Statistics for Non-Imputed Rows:")

## [1] "Descriptive Statistics for Non-Imputed Rows:"

print(non_imputed_stats)

## # A tibble: 1 × 5
##   Life_Satisfaction_Mean Life_Satisfaction_Median Health_Satisfaction_Mean
##                    <dbl>                    <dbl>                    <dbl>
## 1                   7.21                        8                     6.79
## # ℹ 2 more variables: Health_Satisfaction_Median <dbl>, Count <int>

# The imputed observations display slighly larger health & life-satisfaction

# Step 5: Visualizations
# All Rows: Life Satisfaction
ggplot(main, aes(x = factor(life_satisfaction))) +
  geom_bar(fill = "skyblue", color = "black") +
  labs(
    title = "Life Satisfaction - All Rows",
    x = "Life Satisfaction (0-10)",
    y = "Count"
  ) +
  theme_minimal()

# Imputed Rows Only
ggplot(main %>% filter(imputed_flag_life == 1), aes(x = factor(life_satisfaction))) +
  geom_bar(fill = "orange", color = "black") +
  labs(
    title = "Life Satisfaction - Imputed Rows",
    x = "Life Satisfaction (0-10)",
    y = "Count"
  ) +
  theme_minimal()

# Non-Imputed Rows Only
ggplot(main %>% filter(imputed_flag_life == 0), aes(x = factor(life_satisfaction))) +
  geom_bar(fill = "green", color = "black") +
  labs(
    title = "Life Satisfaction - Non-Imputed Rows",
    x = "Life Satisfaction (0-10)",
    y = "Count"
  ) +
  theme_minimal()

# All Rows: Health Satisfaction
ggplot(main, aes(x = factor(health_satisfaction))) +
  geom_bar(fill = "coral", color = "black") +
  labs(
    title = "Health Satisfaction - All Rows",
    x = "Health Satisfaction (0-10)",
    y = "Count"
  ) +
  theme_minimal()

# Imputed Rows Only
ggplot(main %>% filter(imputed_flag_health == 1), aes(x = factor(health_satisfaction))) +
  geom_bar(fill = "orange", color = "black") +
  labs(
    title = "Health Satisfaction - Imputed Rows",
    x = "Health Satisfaction (0-10)",
    y = "Count"
  ) +
  theme_minimal()

# Non-Imputed Rows Only
ggplot(main %>% filter(imputed_flag_health == 0), aes(x = factor(health_satisfaction))) +
  geom_bar(fill = "green", color = "black") +
  labs(
    title = "Health Satisfaction - Non-Imputed Rows",
    x = "Health Satisfaction (0-10)",
    y = "Count"
  ) +
  theme_minimal()

Even though the imputed observations display slightly larger life-satisfaction, the differences in the means and distribution are not large enough to warrant dropping those observations.

3.2.2 Height, Weight, BMI

# Process height and weight
# Track Missing Categories Before Imputation
missing_breakdown_before <- main %>%
  summarise(
    height_NA = sum(is.na(ple0006)),
    height_not_asked = sum(ple0006 %in% c(-8, -5), na.rm = TRUE),
    height_invalid = sum(ple0006 > 245 | (ple0006 < 0 & !(ple0006 %in% c(-8, -5))), na.rm = TRUE),
    weight_NA = sum(is.na(ple0007)),
    weight_not_asked = sum(ple0007 %in% c(-8, -5), na.rm = TRUE),
    weight_invalid = sum(ple0007 < 0 & !(ple0007 %in% c(-8, -5)), na.rm = TRUE)
  )

print("Breakdown of missing and invalid values before imputation:")

## [1] "Breakdown of missing and invalid values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 6
##   height_NA height_not_asked height_invalid weight_NA weight_not_asked
##       <int>            <int>          <int>     <int>            <int>
## 1         0           167036            400         0           167036
## # ℹ 1 more variable: weight_invalid <int>

# Process and Impute Height with Lag/Lead (<= 2 years)
  # Assumption for Imputation of height: does not change significantly for adults
main <- main %>%
  arrange(pid, syear) %>%
  group_by(pid) %>%
  mutate(
    # Track imputation flag for height
    height_imputed = if_else(ple0006 > 245 | ple0006 <= 0 | is.na(ple0006), 1, 0),
    # Set invalid or missing height values to missing
    height = ifelse(ple0006 < 0 | ple0006 > 245, NA, ple0006),
    # Forward fill missing values
    height = zoo::na.locf(height, na.rm = FALSE),

    # Backward fill missing values
    height = zoo::na.locf(height, na.rm = FALSE, fromLast = TRUE)
  ) %>%
  ungroup()

# Process and Impute Weight with Lag/Lead (<= 2 years)
#imputation: The mean weight between the last observation before the missing and the first after. And for the ones that have only one before or one after, the one but only if it is an adjacent year.
main <- main %>%
  filter(!(ple0007 %in% c(-1, -2, -3))) %>%
  group_by(pid) %>%
  arrange(syear, .by_group = TRUE) %>%
  mutate(# Track imputation flag for height
    weight_imputed = if_else(ple0007 <= 0 | is.na(ple0007), 1, 0),
    ple0007 = case_when(ple0007<0 ~ NA_real_,
                             TRUE ~ ple0007), 
    # Create lag and lead weights
    lag_weight = lag(ple0007),
    lead_weight = dplyr::lead(ple0007),
    lag_year = lag(syear),
    lead_year = dplyr::lead(syear),
    
    # Apply imputation rules
    weight = case_when(
      is.na(ple0007) & !is.na(lag_weight) & !is.na(lead_weight) & 
        (syear - lag_year == 1 & lead_year - syear == 1) ~ (lag_weight + lead_weight) / 2, # Mean of valid neighbors
      is.na(ple0007) & !is.na(lag_weight) & (syear - lag_year == 1) ~ lag_weight,         # Use previous value if adjacent
      is.na(ple0007) & !is.na(lead_weight) & (lead_year - syear == 1) ~ lead_weight,     # Use next value if adjacent
      TRUE ~ ple0007  # Keep original if no condition is met
    )
  ) %>%
  select(-lag_weight, -lead_weight, -lag_year, -lead_year) %>%  # Clean up temporary columns
  ungroup()



# Track Missing Categories After Imputation
missing_breakdown_after <- main %>%
  summarise(
    height_NA = sum(is.na(height)),
    weight_NA = sum(is.na(weight)),
    height_imputed = sum(height_imputed),
    weight_imputed = sum(weight_imputed)
  )

print("Breakdown of missing values after imputation:")

## [1] "Breakdown of missing values after imputation:"

print(missing_breakdown_after)

## # A tibble: 1 × 4
##   height_NA weight_NA height_imputed weight_imputed
##       <int>     <int>          <dbl>          <dbl>
## 1     16533     64221         167132         167036

main <- main %>%
  filter(!is.na(height) & !is.na(weight))

# Calculate BMI and Create Categorical Variable
main <- main %>%
  mutate(
    BMI = as.numeric(weight / ((height / 100) ^ 2)),  # Calculate BMI
    bmi_categorical = case_when(
      BMI < 18.5 ~ 1, #underweight
      BMI >= 18.5 & BMI < 25 ~ 2, #normal
      BMI >= 25 & BMI < 30 ~ 3, #overweight
      BMI >= 30 ~ 4, # obese
      TRUE ~ NA_real_
    )
  )

#  Descriptive Statistics for Imputed and Non-Imputed Rows
# Descriptive stats for all rows
all_stats <- main %>%
  summarise(
    Mean = mean(BMI, na.rm = TRUE),
    Median = median(BMI, na.rm = TRUE),
    Q1 = quantile(BMI, 0.25, na.rm = TRUE),
    Q3 = quantile(BMI, 0.75, na.rm = TRUE),
    Min = min(BMI, na.rm = TRUE),
    Max = max(BMI, na.rm = TRUE),
    Count = n()
  )

# Descriptive stats for imputed rows
imputed_stats <- main %>%
  filter(height_imputed == 1 | weight_imputed == 1) %>%
  summarise(
    Mean = mean(BMI, na.rm = TRUE),
    Median = median(BMI, na.rm = TRUE),
    Q1 = quantile(BMI, 0.25, na.rm = TRUE),
    Q3 = quantile(BMI, 0.75, na.rm = TRUE),
    Min = min(BMI, na.rm = TRUE),
    Max = max(BMI, na.rm = TRUE),
    Count = n()
  )

# Descriptive stats for non-imputed rows
non_imputed_stats <- main %>%
  filter(height_imputed == 0 & weight_imputed == 0) %>%
  summarise(
    Mean = mean(BMI, na.rm = TRUE),
    Median = median(BMI, na.rm = TRUE),
    Q1 = quantile(BMI, 0.25, na.rm = TRUE),
    Q3 = quantile(BMI, 0.75, na.rm = TRUE),
    Min = min(BMI, na.rm = TRUE),
    Max = max(BMI, na.rm = TRUE),
    Count = n()
  )

print("Descriptive Statistics for All Rows:")

## [1] "Descriptive Statistics for All Rows:"

print(all_stats)

## # A tibble: 1 × 7
##    Mean Median    Q1    Q3   Min   Max  Count
##   <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>  <int>
## 1  26.1   25.4  22.7  28.7  11.0  197. 217781

print("Descriptive Statistics for Imputed Rows:")

## [1] "Descriptive Statistics for Imputed Rows:"

print(imputed_stats)

## # A tibble: 1 × 7
##    Mean Median    Q1    Q3   Min   Max  Count
##   <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>  <int>
## 1  26.2   25.5  22.8  28.7  11.5  180. 102850

print("Descriptive Statistics for Non-Imputed Rows:")

## [1] "Descriptive Statistics for Non-Imputed Rows:"

print(non_imputed_stats)

## # A tibble: 1 × 7
##    Mean Median    Q1    Q3   Min   Max  Count
##   <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>  <int>
## 1  26.1   25.4  22.7  28.6  11.0  197. 114931

# Step 7: Visualizations
# Histogram for all rows
ggplot(main, aes(x = BMI)) +
  geom_histogram(binwidth = 1, fill = "purple", color = "black", alpha = 0.7) +
  labs(
    title = "BMI Distribution - All Rows",
    x = "BMI",
    y = "Count"
  ) +
  theme_minimal()

# Histogram for imputed rows
ggplot(main %>% filter(height_imputed == 1 | weight_imputed == 1), aes(x = BMI)) +
  geom_histogram(binwidth = 1, fill = "orange", color = "black", alpha = 0.7) +
  labs(
    title = "BMI Distribution - Imputed Rows",
    x = "BMI",
    y = "Count"
  ) +
  theme_minimal()

# Histogram for non-imputed rows
ggplot(main %>% filter(height_imputed == 0 & weight_imputed == 0), aes(x = BMI)) +
  geom_histogram(binwidth = 1, fill = "green", color = "black", alpha = 0.7) +
  labs(
    title = "BMI Distribution - Non-Imputed Rows",
    x = "BMI",
    y = "Count"
  ) +
  theme_minimal()

The imputed and non-imputed rows show almost no relevant differences in the descriptive statistics and the distribution of BMI and height. This indicates that the imputation process did not introduce any significant bias or distortion to the data.

3.2.3 Smoking

Number of Cigarettes has too little observations which is why we are going to use the smoking status as a proxy for smoking. We will create a dummy variable for smoking status and impute missing values using the lag and lead method.

# Create `smoking_dummy`
# Track Missing Categories Before Imputation
missing_breakdown_before <- main %>%
  summarise(
    ple0081_h_NA = sum(is.na(ple0081_h)),
    ple0081_h_not_asked = sum(ple0081_h %in% c(-5, -8), na.rm = TRUE),
    ple0081_h_invalid = sum(ple0081_h < 0 & !(ple0081_h %in% c(-8, -5)), na.rm = TRUE)
  )

print("Breakdown of missing and invalid values before imputation:")

## [1] "Breakdown of missing and invalid values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 3
##   ple0081_h_NA ple0081_h_not_asked ple0081_h_invalid
##          <int>               <int>             <int>
## 1            0              104642               106

# Drop those who refused to answer or answered invalidly
main <- main %>%
  filter(!(ple0081_h %in% c(-1, -3) | ple0086_v4 %in% c(-1, -3))) # 137 observations

# Impute Smoking Status (ple0081_h) with Lag and Lead (Max 2 Years)
main <- main %>%
  arrange(pid, syear) %>%
  group_by(pid) %>%
  mutate(
    # Flag missing smoking values
    smoking_imputed = if_else(ple0081_h %in% c(-5, -8), 1, 0),

    # Determine if the individual was ever observed to smoke
    ever_smoked = any(ple0081_h == 1, na.rm = TRUE),

    # Impute smoking values
    ple0081_h = case_when(
      # If missing and the person ever smoked, impute using lag/lead within 2 years
      ple0081_h %in% c(-5, -8) & ever_smoked ~ {
        lag_val <- if_else(syear - lag(syear) <= 2, lag(ple0081_h), NA_real_)
        lead_val <- if_else(dplyr::lead(syear) - syear <= 2, dplyr::lead(ple0081_h), NA_real_)
        if_else(
          !is.na(lag_val) & !is.na(lead_val),
          (lag_val + lead_val) / 2,
          coalesce(lag_val, lead_val)
        )
      },
      # If missing and the person never smoked, set to 2
      ple0081_h %in% c(-5, -8) & !ever_smoked ~ 2,

      # Keep observed positive smoking values
      ple0081_h > 0 ~ ple0081_h,

      # Set other invalid cases to NA
      TRUE ~ NA_real_
    ),

    # Create smoking dummy (1 = Smoker, 0 = Non-Smoker)
    smoking_dummy = case_when(
      ple0081_h <= 1.5 ~ 1,
      ple0081_h > 1.5 ~ 0,
      TRUE ~ NA_real_
    )
  ) %>%
  ungroup()


# Remove Remaining Invalid or Negative Values
main <- main %>%
  filter(!is.na(smoking_dummy))

# Descriptive Statistics
# Smoking Dummy
smoking_stats_all <- main %>%
  summarise(
    Mean_Smoking = mean(smoking_dummy, na.rm = TRUE),
    Count = n()
  )

smoking_stats_imputed <- main %>%
  filter(smoking_imputed == 1) %>%
  summarise(
    Mean_Smoking = mean(smoking_dummy, na.rm = TRUE),
    Count = n()
  )

smoking_stats_non_imputed <- main %>%
  filter(smoking_imputed == 0) %>%
  summarise(
    Mean_Smoking = mean(smoking_dummy, na.rm = TRUE),
    Count = n()
  )

print("Descriptive Statistics for Smoking (All Rows):")

## [1] "Descriptive Statistics for Smoking (All Rows):"

print(smoking_stats_all)

## # A tibble: 1 × 2
##   Mean_Smoking  Count
##          <dbl>  <int>
## 1        0.306 217644

print("Descriptive Statistics for Smoking (Imputed Rows):")

## [1] "Descriptive Statistics for Smoking (Imputed Rows):"

print(smoking_stats_imputed)

## # A tibble: 1 × 2
##   Mean_Smoking  Count
##          <dbl>  <int>
## 1        0.347 104642

print("Descriptive Statistics for Smoking (Non-Imputed Rows):")

## [1] "Descriptive Statistics for Smoking (Non-Imputed Rows):"

print(smoking_stats_non_imputed)

## # A tibble: 1 × 2
##   Mean_Smoking  Count
##          <dbl>  <int>
## 1        0.269 113002

# Visualizations
# Smoking Dummy
ggplot(main, aes(x = factor(smoking_dummy))) +
  geom_bar(fill = "skyblue", color = "black") +
  labs(title = "Smoking Status - All Rows", x = "Smoking Status (1 = Yes, 0 = No)", y = "Count") +
  theme_minimal()

ggplot(main %>% filter(smoking_imputed == 1), aes(x = factor(smoking_dummy))) +
  geom_bar(fill = "orange", color = "black") +
  labs(title = "Smoking Status - Imputed Rows", x = "Smoking Status (1 = Yes, 0 = No)", y = "Count") +
  theme_minimal()

ggplot(main %>% filter(smoking_imputed == 0), aes(x = factor(smoking_dummy))) +
  geom_bar(fill = "green", color = "black") +
  labs(title = "Smoking Status - Non-Imputed Rows", x = "Smoking Status (1 = Yes, 0 = No)", y = "Count") +
  theme_minimal()

As the imputed rows show a noticably larger share of smokers, this should be kept in mind for the analysis as we might overestimate smoking. However, the imputation is necessary to keep the sample size large enough for the analysis.

3.2.4 Diet

We decided not to include the diet variable in the analysis as it is only available for a very small subset of the sample (surveyed only every second year from 2004-2014). This would lead to a significant reduction in the sample size and might introduce bias.

4. Control Variables

4.1 Worries about job security, financial situation, and economic situation

# Create variables for worries about job security, financial situation, and economic situation
# Track Missing Categories Before Imputation
missing_breakdown_before <- main %>%
  summarise(
    plh0042_refused = sum(plh0042 == -1, na.rm = TRUE),
    plh0042_NA = sum(plh0042 %in% c(-5, -6), na.rm = TRUE),
    plh0042_not_applicable = sum(plh0042 == -2, na.rm = TRUE),
    plh0033_refused = sum(plh0033 == -1, na.rm = TRUE),
    plh0033_invalid = sum(plh0033 == -2, na.rm = TRUE),
    plh0032_NA = sum(plh0032  == -5, na.rm = TRUE),
    plh0032_invalid = sum(plh0032  == -1, na.rm = TRUE)
  )

print("Breakdown of missing values before imputation:")

## [1] "Breakdown of missing values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 7
##   plh0042_refused plh0042_NA plh0042_not_applicable plh0033_refused
##             <int>      <int>                  <int>           <int>
## 1            4352       3398                  80367             340
## # ℹ 3 more variables: plh0033_invalid <int>, plh0032_NA <int>,
## #   plh0032_invalid <int>

# Lag/Lead Imputation (Max 2 Years)
main <- main %>%
  filter(plh0033 != -1 & plh0042 != -1 & plh0032  != -1 & plh0033 != -2 & plh0032 != -2) %>% # drop those who refused to answer or answered invalid
  arrange(pid, syear) %>%  # Ensure data is ordered by pid and syear
  group_by(pid) %>%
  mutate(
    # Impute -5 or -8 for `plh0042` with max 2-year lag/lead
    worries_job_imputed = if_else(plh0042 %in% c(-5, -6), 1, 0),
    plh0042 = case_when(
      plh0042 %in% c(-5, -6) ~ {
        lag_val <- if_else(syear - lag(syear) <= 2, lag(plh0042), NA_real_)
        lead_val <- if_else(dplyr::lead(syear) - syear <= 2, dplyr::lead(plh0042), NA_real_)
        if_else(!is.na(lag_val) & !is.na(lead_val), (lag_val + lead_val) / 2, coalesce(lag_val, lead_val))
      },
      plh0042 == -2 ~ 3,
      TRUE ~ plh0042
    ),
    # not necessary for plh0033 because no remaining missings
    # Repeat for `plh0032`
    worries_economic_imputed = if_else(plh0032 == -5, 1, 0),
    plh0032 = case_when(
      plh0032 == -5 ~ {
        lag_val <- if_else(syear - lag(syear) <= 2, lag(plh0032), NA_real_)
        lead_val <- if_else(dplyr::lead(syear) - syear <= 2, dplyr::lead(plh0032), NA_real_)
        if_else(!is.na(lag_val) & !is.na(lead_val), (lag_val + lead_val) / 2, coalesce(lag_val, lead_val))
      },
      TRUE ~ plh0032
    )
  ) %>%
  ungroup() 

# Create Categorical and Dummy Variables
main <- main %>%
  filter(plh0032 != -5 & plh0042 != -5 & plh0042 != -6) %>% # drop those who couldnt be imputed
  mutate(
    worr_job_categorical = case_when(plh0042 == 1 ~ 3, # no worries
                                     plh0042 == 3 ~ 1, # large worries
                                     TRUE ~ plh0042),
    worr_financial_categorical = case_when(plh0033 == 1 ~ 3, # no worries
                                          plh0033 == 3 ~ 1, # large worries
                                          TRUE ~ plh0033),
    worr_economic_categorical = case_when(plh0032 == 1 ~ 3, # no worries
                                          plh0032 == 3 ~ 1, # large worries
                                          TRUE ~ plh0032),
    worr_job_dummy = ifelse(worr_job_categorical >= 2, 1, 0),
    worr_financial_dummy = ifelse(worr_financial_categorical >= 2, 1, 0),
    worr_economic_dummy = ifelse(worr_economic_categorical >= 2, 1, 0)
  )

main <- main %>%
  filter(!is.na(worr_job_categorical) & !is.na(worr_financial_categorical)& !is.na(worr_economic_categorical))

Descriptive Statistics

# Define descriptive_stats function
unique(main$worr_economic_dummy)

## [1] 1 0

descriptive_stats <- function(data, condition) {
  data %>%
    filter(!!rlang::enquo(condition)) %>%  # Use enquo for capturing condition
    summarise(
      Job_Worries_Mean = mean(as.numeric(worr_job_dummy), na.rm = TRUE),
      Financial_Worries_Mean = mean(as.numeric(worr_financial_dummy), na.rm = TRUE),
      Economic_Worries_Mean = mean(as.numeric(worr_economic_dummy), na.rm = TRUE),
      Count = n()
    )
}
# Calculate statistics for all rows, imputed rows, and non-imputed rows
all_stats <- descriptive_stats(main, TRUE)
imputed_stats <- descriptive_stats(main, worries_job_imputed == 1 | worries_economic_imputed == 1)
non_imputed_stats <- descriptive_stats(main, worries_job_imputed == 0 & worries_economic_imputed == 0)

print("Descriptive Statistics for All Rows:")

## [1] "Descriptive Statistics for All Rows:"

print(all_stats)

## # A tibble: 1 × 4
##   Job_Worries_Mean Financial_Worries_Mean Economic_Worries_Mean  Count
##              <dbl>                  <dbl>                 <dbl>  <int>
## 1            0.273                  0.660                 0.819 209333

print("Descriptive Statistics for Imputed Rows:")

## [1] "Descriptive Statistics for Imputed Rows:"

print(imputed_stats)

## # A tibble: 1 × 4
##   Job_Worries_Mean Financial_Worries_Mean Economic_Worries_Mean Count
##              <dbl>                  <dbl>                 <dbl> <int>
## 1            0.365                  0.726               0.00991  2219

print("Descriptive Statistics for Non-Imputed Rows:")

## [1] "Descriptive Statistics for Non-Imputed Rows:"

print(non_imputed_stats)

## # A tibble: 1 × 4
##   Job_Worries_Mean Financial_Worries_Mean Economic_Worries_Mean  Count
##              <dbl>                  <dbl>                 <dbl>  <int>
## 1            0.272                  0.659                 0.827 207114

# Visualizations
# Drop rows with NAs in worry-related columns
main <- main %>%
  drop_na(worr_job_categorical, worr_financial_categorical, worr_economic_categorical)

# Distribution of Worry Levels - All Rows
main %>%
  select(worr_job_categorical, worr_financial_categorical, worr_economic_categorical) %>%
  pivot_longer(cols = everything(), names_to = "Worry_Type", values_to = "Worry_Level") %>%
  ggplot(aes(x = Worry_Level, fill = Worry_Type)) +
  geom_bar(position = "dodge", color = "black") +
  labs(
    title = "Distribution of Worry Levels - All Rows",
    x = "Worry Level",
    y = "Count",
    fill = "Worry Type"
  ) +
  theme_minimal()

# Imputed Rows
main %>%
  filter(worries_job_imputed == 1 | worries_economic_imputed == 1) %>%
  pivot_longer(cols = c(worr_job_categorical, worr_economic_categorical), 
               names_to = "Worry_Type", values_to = "Worry_Level") %>%
  ggplot(aes(x = Worry_Level, fill = Worry_Type)) +
  geom_bar(position = "dodge", color = "black") +
  labs(
    title = "Distribution of Worry Levels - Imputed Rows",
    x = "Worry Level",
    y = "Count",
    fill = "Worry Type"
  ) +
  theme_minimal()

# Non-Imputed Rows
main %>%
  filter(worries_job_imputed == 0 & worries_economic_imputed == 0) %>%
  pivot_longer(cols = c(worr_job_categorical, worr_economic_categorical), 
               names_to = "Worry_Type", values_to = "Worry_Level") %>%
  ggplot(aes(x = Worry_Level, fill = Worry_Type)) +
  geom_bar(position = "dodge", color = "black") +
  labs(
    title = "Distribution of Worry Levels - Non-Imputed Rows",
    x = "Worry Level",
    y = "Count",
    fill = "Worry Type"
  ) +
  theme_minimal()

4.2 Tenure

# Breakdown Before Imputation
missing_breakdown_before <- main %>%
  summarise(
    refused = sum(pgerwzeit %in% c(-1, -3), na.rm = TRUE),
    not_applicable = sum(pgerwzeit == -2, na.rm = TRUE)
  )

print("Breakdown of missing values before imputation:")

## [1] "Breakdown of missing values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 2
##   refused not_applicable
##     <int>          <int>
## 1     112          84749

# Clean Tenure
main <- main %>%
  filter(pgerwzeit != -1 & pgerwzeit != -3) %>% # drop those who refused or answered invalidly
  mutate(tenure = case_when(pgerwzeit == -2 ~ 0, # impute those who are without a job
                            TRUE ~ pgerwzeit))

# Visualizations
# All Rows
ggplot(main, aes(x = tenure)) +
  geom_histogram(binwidth = 1, fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Tenure - All Rows",
    x = "Tenure (Years)",
    y = "Count"
  ) +
  theme_minimal()

4.3 Net Income and Working time per week

#### Net Income

# Breakdown Before Imputation for income
missing_breakdown_before <- main %>%
  summarise(
    refused = sum(pglabnet %in% c(-1, -3), na.rm = TRUE), 
    not_applicable = sum(pglabnet == -2, na.rm = TRUE)
  )

print("Breakdown of missing values before imputation:")

## [1] "Breakdown of missing values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 2
##   refused not_applicable
##     <int>          <int>
## 1       0          83777

# Transform `pglabnet` into `net_income`
main <- main %>%
  mutate(net_income = case_when(pglabnet == -2 ~ 0, # impute those who are without a job
                            TRUE ~ pglabnet))

#### Working time per week

# Breakdown Before Imputation for work time
missing_breakdown_before <- main %>%
  summarise(
    refused = sum(pgtatzeit %in% c(-1, -3), na.rm = TRUE),
    not_applicable = sum(pgtatzeit == -2, na.rm = TRUE)
  )

print("Breakdown of missing values before imputation:")

## [1] "Breakdown of missing values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 2
##   refused not_applicable
##     <int>          <int>
## 1    3687          83776

# Transform `pgtatzeit` into `work_time_weekly`
main <- main %>%
  filter(pgtatzeit != -1 & pgtatzeit != -3) %>% # drop those who refused or answered invalidly
  mutate(
    work_time_weekly = case_when(pgtatzeit == -2 ~ 0, # impute those who are without a job
                            TRUE ~ pgtatzeit))

# Summary Statistics for Net Income
# All rows
net_income_all <- main %>%
  summarise(
    Mean = mean(net_income, na.rm = TRUE),
    Median = median(net_income, na.rm = TRUE),
    Min = min(net_income, na.rm = TRUE),
    Max = max(net_income, na.rm = TRUE),
    Count = sum(!is.na(net_income))
  )


# Summary Statistics for Work Time Weekly
# All rows
work_time_all <- main %>%
  summarise(
    Mean = mean(work_time_weekly, na.rm = TRUE),
    Median = median(work_time_weekly, na.rm = TRUE),
    Min = min(work_time_weekly, na.rm = TRUE),
    Max = max(work_time_weekly, na.rm = TRUE),
    Count = sum(!is.na(work_time_weekly))
  )

# Display Results
print("Net Income Summary Statistics - All Rows:")

## [1] "Net Income Summary Statistics - All Rows:"

print(net_income_all)

## # A tibble: 1 × 5
##    Mean Median Min       Max        Count
##   <dbl>  <dbl> <dbl+lbl> <dbl+lbl>  <int>
## 1 1046.    563 0         124219    205534

print("\n Work Time Weekly Summary Statistics - All Rows:")

## [1] "\n Work Time Weekly Summary Statistics - All Rows:"

print(work_time_all)

## # A tibble: 1 × 5
##    Mean Median Min       Max        Count
##   <dbl>  <dbl> <dbl+lbl> <dbl+lbl>  <int>
## 1  22.2     22 0         80        205534

# Plot for Net Income - All Rows
ggplot(main, aes(x = net_income)) +
  geom_histogram(binwidth = 500, fill = "skyblue", color = "black", alpha = 0.7) +
  labs(
    title = "Net Income Distribution - All Rows",
    x = "Net Income",
    y = "Frequency"
  ) +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5))

# Plot for Work Time Weekly - All Rows
ggplot(main, aes(x = work_time_weekly)) +
  geom_histogram(binwidth = 5, fill = "lightcoral", color = "black", alpha = 0.7) +
  labs(
    title = "Work Time Weekly Distribution - All Rows",
    x = "Work Time (Hours/Week)",
    y = "Frequency"
  ) +
  theme_minimal() +
  theme(plot.title = element_text(hjust = 0.5))

4.4 Unemployment

# Transform total years unemployed (pgexpue)
# Breakdown Before Imputation
missing_breakdown_before <- main %>%
  summarise(
    not_answered = sum(pgexpue == -1 , na.rm = TRUE)) # 1278

print("Breakdown of missing values before imputation:")

## [1] "Breakdown of missing values before imputation:"

print(missing_breakdown_before)

## # A tibble: 1 × 1
##   not_answered
##          <int>
## 1         1119

# Clean Total Years Unemployment
main <- main %>%
  rename(total_years_unemployment = pgexpue) %>%
  filter(total_years_unemployment != -1) # drop those who refused

# Visualizations
# All Rows
ggplot(main, aes(x = total_years_unemployment)) +
  geom_histogram(binwidth = 1, fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Total Years Unemployed - All Rows",
    x = "Total Years Unemployed",
    y = "Count"
  ) +
  theme_minimal()

4.5 Occupational Status

# Transform occupational status (pgstib)
main <- main %>%
  filter(pgstib != -1) %>% # drop those who refused
  mutate(
    occup_status = case_when(
      pgstib >= 210 & pgstib <= 250 ~ "Blue Collar Employee",  # Blue collar emp
      pgstib >= 510 & pgstib <= 550 ~ "White Collar Employee",  # White collar emp
      pgstib >= 310 & pgstib <= 340 ~ "Agricultural Employee", # agriculture emp
      pgstib >= 410 & pgstib <= 413 ~ "Agriculture - Self-Employed", # agriculture self-emp
      pgstib >= 610 & pgstib <= 640 ~ "Public Servant",  # Public servant
      (pgstib >= 420 & pgstib <= 433) | pgstib == 560 ~ "White Collar - Self-Employed",  # Self-employed
      pgstib %in% c(12, -2, 10) ~ "Unemployed",  # Unemployed
      pgstib %in% c(11, 15) | (pgstib >= 110 & pgstib <= 150) ~ "Apprentice",  # Apprentice
      pgstib == 13 ~ "Retired",  # Retired
      TRUE ~ "Other"  # Assign a default category for unmatched values
    )
  )


main <- main %>%
  mutate(unemp_dummy = ifelse(occup_status == "Unemployed", 1, 0))


#Visualisation: Bar Plot
ggplot(main, aes(x = occup_status)) +
  geom_bar(fill = "darkred", color = "black") +
  labs(
    title = "Distribution of Occupational Status",
    x = "Occupational Status",
    y = "Count"
  ) +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

4.6 Gender

# Transform sex into male dummy
main <- main %>%
  filter(sex != -3) %>% # drop those who answered invalidly
  mutate(male = ifelse(sex == 1, 1, 0))

#Visualisation: Pie Chart
main %>%
  group_by(male) %>%
  summarize(count = n()) %>%
  mutate(
    proportion = count / sum(count),
    label = paste0(round(proportion * 100, 1), "%")
  ) %>%
  ggplot(aes(x = "", y = proportion, fill = factor(male, labels = c("Female", "Male")))) +
  geom_bar(stat = "identity", width = 1) +
  coord_polar("y") +
  labs(
    title = "Proportion of Male vs. Female",
    fill = "Gender"
  ) +
  theme_minimal() +
  geom_text(aes(label = label), position = position_stack(vjust = 0.5))

4.7 Migration Background

# Transform migration background and create dummy
main <- main %>%
  mutate(germborn = ifelse(migback == 2, 0, 1),
         migback=ifelse(migback >= 2, 1, 0))

#Visualisation: Bar plot
ggplot(main, aes(x = migback)) +
  geom_bar(fill = "cyan", color = "black") +
  labs(
    title = "Distribution of Migration Background",
    x = "Migration Background",
    y = "Count"
  ) +
  theme_minimal()

4.8 Marital Status

# Count the number of NA rows before imputation
na_count_before <- sum(main$pgfamstd == -5)
print(paste("Number of NA rows in pgfamstd_dummy before imputation:", na_count_before))

## [1] "Number of NA rows in pgfamstd_dummy before imputation: 2"

  # depending on that make imputation
# Transform marital status and handle NA with lag/lead logic
main <- main %>%
  filter(pgfamstd != -1 & pgfamstd != -3) %>% # drop those who refused or answered invalidly
  mutate(rel_status = case_when(pgfamstd == 1 | pgfamstd == 7  ~ "married",
                                pgfamstd == 2 | pgfamstd == 8  ~ "separated",
                                pgfamstd == 3 ~ "single",
                                pgfamstd == 4 ~ "divorced",
                                pgfamstd == 5 ~ "widowed",
                                pgfamstd == 6 ~ "spouse abroad",
                                TRUE ~ NA_character_),
         rel_status = factor(rel_status))

sum(is.na(main$rel_status))

## [1] 2

# Drop the two missings because relationship status is too fluctuating to impute reasonably
main <- main %>%
  filter(!is.na(rel_status))


# Visualizations
# All Rows
ggplot(main, aes(x = rel_status)) +
  geom_bar(fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Relationship Status - All Rows",
    x = "Relationship Status",
    y = "Count"
  ) +
  theme_minimal()

4.9 Age

We restrict or analysis to those between 25 and 55 years old. This is reasonable as both during growth (until age 25) and during old age, individuals likeley display different health patterns.

main <- main %>%
  filter(gebjahr != -1) %>% # drop those who refused
  mutate(age = syear - gebjahr)

# Visualizations
# All Rows
ggplot(main, aes(x = age)) +
  geom_histogram(binwidth = 1, fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Agge",
    x = "Age",
    y = "Count"
  ) +
  theme_minimal()

# Filter for age between 25 and 55
main <- main %>%
  filter(age >= 25 & age <= 55)

ggplot(main, aes(x = age)) +
  geom_histogram(binwidth = 1, fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Agge",
    x = "Age",
    y = "Count"
  ) +
  theme_minimal()

4.10 Education

We decide to include and impute education after applying the age restriction as education is likely to be more stable after age 25.

main <- main %>%
  mutate(educ = as.numeric(pgisced11),
         educ = case_when(educ < 0 ~ NA_real_,
                             TRUE ~ educ))
main <- main %>%
  mutate(educ_imputed = ifelse(is.na(educ), 1,0)) %>%
  arrange(pid, syear) %>%  # Ensure data is sorted properly
  group_by(pid) %>%
  fill(educ, .direction = "down") %>%  # Carry forward values
  fill(educ, .direction = "up") %>% #also carry upward because all observations are older than 25
  ungroup() %>%
  filter(!is.na(educ)) 

# Labels
# [1] Primary education 
#           [2] Lower secondary education 
#           [3] Upper secondary education 
# [4] Post-secondary non-tertiary educati 
#      [5] Short-cycle tertiary education 
#      [6] Bachelor s or equivalent level 
#        [7] Master s or equivalent level 
#        [8] Doctoral or equivalent level 

# All Rows
ggplot(main, aes(x = educ)) +
  geom_bar(fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Education Level - All Rows",
    x = "Education Level",
    y = "Count"
  ) +
  theme_minimal()

# Imputed Rows only
main %>%
  filter(educ_imputed == 1) %>%
  ggplot(aes(x = educ)) +
  geom_bar(fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Education Level - Imputed Rows",
    x = "Education Level",
    y = "Count"
  ) +
  theme_minimal()

# Non-Imputed Rows only
main %>%
  filter(educ_imputed == 0) %>%
  ggplot(aes(x = educ)) +
  geom_bar(fill = "skyblue", color = "black") +
  labs(
    title = "Distribution of Education Level - Not Imputed Rows",
    x = "Education Level",
    y = "Count"
  ) +
  theme_minimal()

Final Cleanup: Keeping relevant & cleaned variables

# Select only the relevant cleaned variables
main <- main %>%
  select(
    pid, syear, gebjahr, migback, germborn, health, worr_health_categorical,
    total_years_unemployment, worr_health_dummy, health_in_2yrs, health_decline_2yrs,
    life_satisfaction, health_satisfaction, height, weight, BMI, bmi_categorical,
    smoking_dummy, ever_smoked, worr_job_categorical, worr_financial_categorical, worr_economic_categorical, worr_job_dummy, worr_financial_dummy,worr_economic_dummy,
    tenure, net_income, work_time_weekly, occup_status, unemp_dummy, male, rel_status,
    age, educ
  )

# Count missing values for each column
missing_counts <- colSums(is.na(main))

# View the result
missing_counts

##                        pid                      syear 
##                          0                          0 
##                    gebjahr                    migback 
##                          0                          0 
##                   germborn                     health 
##                          0                          0 
##    worr_health_categorical   total_years_unemployment 
##                          0                          0 
##          worr_health_dummy             health_in_2yrs 
##                          0                      17272 
##        health_decline_2yrs          life_satisfaction 
##                      17272                          0 
##        health_satisfaction                     height 
##                          0                          0 
##                     weight                        BMI 
##                          0                          0 
##            bmi_categorical              smoking_dummy 
##                          0                          0 
##                ever_smoked       worr_job_categorical 
##                          0                          0 
## worr_financial_categorical  worr_economic_categorical 
##                          0                          0 
##             worr_job_dummy       worr_financial_dummy 
##                          0                          0 
##        worr_economic_dummy                     tenure 
##                          0                          0 
##                 net_income           work_time_weekly 
##                          0                          0 
##               occup_status                unemp_dummy 
##                          0                          0 
##                       male                 rel_status 
##                          0                          0 
##                        age                       educ 
##                          0                          0

# Count values below 0 for each column
below_zero_counts <- colSums(main < 0, na.rm = TRUE)

## Warning in Ops.factor(left, right): '<' not meaningful for factors

# View the result
below_zero_counts

##                        pid                      syear 
##                          0                          0 
##                    gebjahr                    migback 
##                          0                          0 
##                   germborn                     health 
##                          0                          0 
##    worr_health_categorical   total_years_unemployment 
##                          0                          0 
##          worr_health_dummy             health_in_2yrs 
##                          0                          0 
##        health_decline_2yrs          life_satisfaction 
##                          0                          0 
##        health_satisfaction                     height 
##                          0                          0 
##                     weight                        BMI 
##                          0                          0 
##            bmi_categorical              smoking_dummy 
##                          0                          0 
##                ever_smoked       worr_job_categorical 
##                          0                          5 
## worr_financial_categorical  worr_economic_categorical 
##                          0                       1679 
##             worr_job_dummy       worr_financial_dummy 
##                          0                          0 
##        worr_economic_dummy                     tenure 
##                          0                          0 
##                 net_income           work_time_weekly 
##                          0                          0 
##               occup_status                unemp_dummy 
##                          0                          0 
##                       male                 rel_status 
##                          0                          0 
##                        age                       educ 
##                          0                          0

main <- main %>%
  filter(!is.na(health_decline_2yrs) & !is.na(health_in_2yrs) & worr_job_categorical > 0 & worr_economic_categorical > 0) # drop those who are still missing and were kept before to facilitate impuatation

#Display the summary of the dataset
skim(main)

Data summary
Name	main
Number of rows	74326
Number of columns	34
_______________________
Column type frequency:
character	1
factor	1
logical	1
numeric	31
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
occup_status	0	1	5	28	0	9	0

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
rel_status	0	1	FALSE	6	mar: 46899, sin: 17549, div: 6969, sep: 2166

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
ever_smoked	0	1	0.42	FAL: 42994, TRU: 31332

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
pid	1	10929626.47	11544005.60	5201.00	2532901.00	5028152.00	21143401.00	38681902.00	▇▁▂▁▁
syear	1	2011.23	5.23	2001.00	2007.00	2012.00	2016.00	2019.00	▅▅▅▇▇
gebjahr	1	1970.23	8.83	1955.00	1963.00	1969.00	1977.00	1994.00	▅▇▆▃▁
migback	1	0.19	0.40	0.00	0.00	0.00	0.00	1.00	▇▁▁▁▂
germborn	1	0.85	0.35	0.00	1.00	1.00	1.00	1.00	▂▁▁▁▇
health	1	3.56	0.89	1.00	3.00	4.00	4.00	5.00	▁▂▅▇▂
worr_health_categorical	1	1.79	0.67	1.00	1.00	2.00	2.00	3.00	▆▁▇▁▂
total_years_unemployment	1	1.00	2.52	0.00	0.00	0.00	0.75	37.00	▇▁▁▁▁
worr_health_dummy	1	0.65	0.48	0.00	0.00	1.00	1.00	1.00	▅▁▁▁▇
health_in_2yrs	1	3.51	0.89	1.00	3.00	4.00	4.00	5.00	▁▂▅▇▂
health_decline_2yrs	1	0.25	0.43	0.00	0.00	0.00	0.00	1.00	▇▁▁▁▂
life_satisfaction	1	7.23	1.68	0.00	7.00	8.00	8.00	10.00	▁▁▂▇▃
health_satisfaction	1	6.99	2.05	0.00	6.00	7.00	8.00	10.00	▁▂▃▇▃
height	1	172.71	9.48	82.00	165.00	172.00	180.00	210.00	▁▁▁▇▁
weight	1	77.97	17.63	34.00	65.00	76.00	88.00	230.00	▇▇▁▁▁
BMI	1	26.04	5.14	12.03	22.58	25.24	28.41	197.23	▇▁▁▁▁
bmi_categorical	1	2.68	0.78	1.00	2.00	3.00	3.00	4.00	▁▇▁▆▃
smoking_dummy	1	0.37	0.48	0.00	0.00	0.00	1.00	1.00	▇▁▁▁▅
worr_job_categorical	1	1.49	0.66	1.00	1.00	1.00	2.00	3.00	▇▁▃▁▁
worr_financial_categorical	1	1.92	0.69	1.00	1.00	2.00	2.00	3.00	▅▁▇▁▃
worr_economic_categorical	1	2.08	0.65	1.00	2.00	2.00	2.00	3.00	▂▁▇▁▃
worr_job_dummy	1	0.39	0.49	0.00	0.00	0.00	1.00	1.00	▇▁▁▁▅
worr_financial_dummy	1	0.72	0.45	0.00	0.00	1.00	1.00	1.00	▃▁▁▁▇
worr_economic_dummy	1	0.83	0.38	0.00	1.00	1.00	1.00	1.00	▂▁▁▁▇
tenure	1	7.93	8.60	0.00	0.67	4.75	13.00	40.92	▇▂▂▁▁
net_income	1	1475.72	1495.12	0.00	450.00	1300.00	2045.00	124219.00	▇▁▁▁▁
work_time_weekly	1	30.97	18.56	0.00	17.00	39.00	43.00	80.00	▅▂▇▂▁
unemp_dummy	1	0.15	0.35	0.00	0.00	0.00	0.00	1.00	▇▁▁▁▂
male	1	0.46	0.50	0.00	0.00	0.00	1.00	1.00	▇▁▁▁▇
age	1	41.00	8.14	25.00	35.00	42.00	48.00	55.00	▅▆▇▇▆
educ	1	4.05	1.60	0.00	3.00	3.00	6.00	8.00	▁▇▂▃▂

Saving the cleaned dataset

# Save the final main dataset as a CSV file
write.csv(main, "SOEP_main_final.csv", row.names = FALSE)

Investigating the dataset

Correlation Heatmap

# In order to identify key predictors and relationships between variables, we create a correlation heatmap between numerical variables
# Select numeric columns
numeric_data <- main[, sapply(main, is.numeric)]

# Calculate correlation matrix
corr_matrix <- cor(numeric_data, use = "complete.obs")

# Plot correlation heatmap
ggcorrplot(corr_matrix, method = "circle", lab = FALSE) +
  labs(title = "Correlation Heatmap") +
  theme_minimal()

# Set correlations below 0.5 or above -0.5 to NA
filtered_corr <- corr_matrix
filtered_corr[abs(filtered_corr) < 0.5] <- NA


# Define pairs to exclude
exclude_pairs <- list(
  c("worr_job_dummy", "worr_job_categorical"),
  c("worr_job_categorical", "worr_job_dummy"),
  c("worr_economic_dummy", "worr_economic_categorical"),
  c("worr_economic_categorical", "worr_economic_dummy"),
  c("worr_health_dummy", "worr_health_categorical"),
  c("worr_health_categorical", "worr_health_dummy"),
  c("bmi_categorical", "BMI"),
  c("BMI", "bmi_categorical"),
  c("BMI", "weight"),
  c("weight", "BMI"),
  c("germborn", "migback"),
  c("migback", "germborn"),
  c("worr_financial_dummy", "worr_financial_categorical"),
  c("worr_financial_categorical", "worr_financial_dummy"),
  c("age", "gebjahr"),
  c("gebjahr", "age"),
  c("bmi_categorical", "weight"),
  c("weight", "bmi_categorical"),
  c("worr_economic_dummy", "worr_economic_categorical"),
  c("health_satisfaction", "health"),
  c("work_time_weekly", "net_income"),
  c("syear", "pid"),
  c("pid", "syear"),
  c("weight", "height"),
  c("worr_health_categorical", "health"),
  c("work_time_weekly", "unemp_dummy"),
  c("life_satisfaction", "health_satisfaction"),
  c("worr_health_categorical", "health_satisfaction"),
  c("health_in_2yrs", "health"),
  c("male", "height"),
  c("health_in_2yrs", "health_satisfaction")
)

filtered_table <- as.data.frame(as.table(filtered_corr)) %>%
  filter(
    !is.na(Freq),  # Exclude NA correlations
    Var1 != Var2,  # Exclude diagonal elements
    !(paste(Var1, Var2, sep = "_") %in% sapply(exclude_pairs, function(x) paste(x[1], x[2], sep = "_")))  # Exclude specific pairs
  ) %>%
  arrange(desc(abs(Freq)))  # Sort by absolute correlation

# View the filtered table
filtered_table  # Display the table

# Create a bar plot
# Rename variables for prettier and clearer names
filtered_table <- filtered_table %>%
  mutate(
    Variable_Pairs = case_when(
      Var1 == "health" & Var2 == "health_satisfaction" ~ "Health & Health Satisfaction",
      Var1 == "height" & Var2 == "male" ~ "Height & Gender (Male)",
      Var1 == "net_income" & Var2 == "work_time_weekly" ~ "Net Income & Work Time Weekly",
      Var1 == "health" & Var2 == "health_in_2yrs" ~ "Health & Health in 2 years",
      Var1 == "height" & Var2 == "weight" ~ "Height & Weight",
      Var1 == "health_satisfaction" & Var2 == "health_in_2yrs" ~ "Health Satisfaction & Health in 2 years",
      Var1 == "health_satisfaction" & Var2 == "life_satisfaction" ~ "Health Satisfaction & Life Satisfaction",
      Var1 == "health_satisfaction" & Var2 == "worr_health_categorical" ~ "Health Satisfaction & Worrying about Health (Categorical)",
      Var1 == "health" & Var2 == "worr_health_categorical" ~ "Health & Worrying about Health (Categorical)",
      Var1 == "unemp_dummy" & Var2 == "work_time_weekly" ~ "Unemployment (Dummy) & Work Time Weekly",
      TRUE ~ paste(Var1, Var2, sep = " & ") 
    )
  )

# Create the bar plot
ggplot(filtered_table, aes(x = reorder(Variable_Pairs, Freq), y = Freq, fill = Freq > 0)) +
  geom_bar(stat = "identity", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Correlation Plot",
    subtitle = "Visualizing selected Correlations"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#163E64"),  # Red for negative, dark blue for positive
    guide = "none"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  
    plot.background = element_rect(fill = "white", color = NA),  

    # Gridlines
    panel.grid.major = element_blank(),  
    panel.grid.minor = element_blank(), 

    # Axis styling
    axis.title.x = element_blank(),  
    axis.title.y = element_blank(),  
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"),  

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)), 
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  
    
    # Legend styling
    legend.position = "none"  
  )

#Save Graph
ggsave("correlation_plot.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

Gender Disparities

# In order to highlight gender disparities in health perceptions, we create these graphs per gender
# Group data by pid and gender (male), and summarize
main_unique <- main %>%
  group_by(pid, male) %>%
  summarize(
    health = mean(health, na.rm = TRUE),
    health_decline_2yrs = mean(health_decline_2yrs, na.rm = TRUE),
    worr_health_dummy = mean(worr_health_dummy, na.rm = TRUE),
    health_satisfaction = mean(health_satisfaction, na.rm = TRUE),
    .groups = "drop"
  )

# Health  per Gender: Violin Plot
ggplot(main_unique, aes(x = factor(male), y = health, fill = factor(male))) +
  geom_violin(trim = FALSE, alpha = 0.7, color = "black") +  
  stat_summary(fun = "mean", geom = "point", shape = 16, size = 3, color = "black") +  # Add mean points
  geom_text(stat = "summary", fun = "mean", aes(label = round(after_stat(y), 2)), vjust = -0.5) +  # Add mean labels
  scale_x_discrete(labels = c("0" = "Female", "1" = "Male")) +  # Update x-axis labels
  scale_fill_manual(values = c("#FF0000", "#163E64")) +  # Red for Female, Dark Blue for Male
  labs(
    title = "Health Distribution by Gender",
    subtitle = "Violin Plot Showing Health Scores",
    x = "Gender",
    y = "Health"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

#Save Graph
ggsave("gender_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_decline_2yrs per Gender: Histogram
ggplot(main_unique, aes(x = factor(male), y = health_decline_2yrs, fill = factor(male))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and define outliers
  scale_fill_manual(values = c("#FF0000", "#163E64"), labels = c("Female", "Male"), name = "Gender") + 
  scale_x_discrete(labels = c("0" = "Female", "1" = "Male")) +  # Update x-axis labels
  labs(
    title = "Health Decline in 2 Years by Gender",
    subtitle = "Boxplot Comparison of Health Decline Across Genders",
    x = "Gender",
    y = "Health Decline"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"
  )

#Save Graph
ggsave("gender_health_decline.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for worr_health_dummy per Gender: Histogram
ggplot(main_unique, aes(x = factor(male), y = worr_health_dummy, fill = factor(male))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and define outliers
  scale_fill_manual(values = c("#FF0000", "#163E64"), labels = c("Female", "Male"), name = "Gender") + 
  scale_x_discrete(labels = c("0" = "Female", "1" = "Male")) +  # Update x-axis labels
  labs(
    title = "Health Worries by Gender",
    subtitle = "Boxplot of Health Worries for Females and Males",
    x = "Gender",
    y = "Health Worries"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "None"
  )

#Save Graph
ggsave("gender_worr_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_satisfaction per Gender: Density plot
ggplot(main_unique, aes(x = health_satisfaction, fill = factor(male), color = factor(male))) +
  geom_density(alpha = 0.5, size = 1) +  # Add transparency and adjust line thickness
  scale_fill_manual(values = c("#FF0000", "#163E64"), labels = c("Female", "Male"), name = "Gender") +  
  scale_color_manual(values = c("#FF0000", "#163E64"), labels = c("Female", "Male"), name = "Gender") +  
  labs(
    title = "Density of Health Satisfaction by Gender",
    subtitle = "Density Plot Comparing Female and Male Responses",
    x = "Health Satisfaction",
    y = "Density",
    fill = "Gender",
    color = "Gender"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"
  )

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

#Save Graph
ggsave("gender_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

We notice that gender differences are largley insignificant on health variables. Men display slightly larger health, health satisfaction and lower worries bout health but these. differences are rather small. We, therefore, do not expect gender to be a strong predictor.

Educational Level Disparities

# Group data by pid and educ, and summarize
main_educ <- main %>%
  group_by(pid, educ) %>%
  summarize(
    health = mean(health, na.rm = TRUE),
    health_decline_2yrs = mean(health_decline_2yrs, na.rm = TRUE),
    worr_health_dummy = mean(worr_health_dummy, na.rm = TRUE),
    health_satisfaction = mean(health_satisfaction, na.rm = TRUE),
    .groups = "drop"
  )
# Count of individuals per Educ
ggplot(main_educ %>% filter(educ != 0), aes(x = factor(educ), fill = factor(educ))) +
  geom_bar(alpha = 0.7, color = "black") +
  scale_x_discrete(
    labels = c(
      "1" = "Primary",
      "2" = "Lower Secondary",
      "3" = "Upper Secondary",
      "4" = "Post-Secondary",
      "5" = "Short-Cycle Tertiary",
      "6" = "Bachelor's",
      "7" = "Master's",
      "8" = "Doctoral"
    ),
    limits = c("1", "2", "3", "4", "5", "6", "7", "8") 
  ) +
  scale_fill_brewer(palette = "RdBu") +  
  labs(
    title = "Distribution of Individuals by Educational Level",
    x = "Educational Level",
    y = "Count",
    fill = "Educational Level"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"
  )

#Save Graph
ggsave("educ.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Health  per Educ: 
ggplot(main_educ %>% filter(educ != 0), aes(x = health, fill = factor(educ))) +
  geom_density(alpha = 0.7, color = "black") +
  facet_wrap(~ factor(educ), ncol = 2, labeller = as_labeller(c(
    "1" = "Primary",
    "2" = "Lower Secondary",
    "3" = "Upper Secondary",
    "4" = "Post-Secondary",
    "5" = "Short-Cycle Tertiary",
    "6" = "Bachelor's",
    "7" = "Master's",
    "8" = "Doctoral"
  ))) +
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Density of Health by Educational Level",
    x = "Health",
    y = "Density",
    fill = "Educational Level"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_blank(),  # Dark blue y-axis labels

    # Facet title styling
    strip.text = element_text(size = 12, face = "bold", color = "#1E2B4F", margin = ggplot2::margin(b = 5)),  # Style facet labels
    
    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
  )

#Save Graph
ggsave("educ_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_decline_2yrs per educ: 
ggplot(main_educ %>% filter(educ != 0), aes(x = factor(educ), y = health_decline_2yrs, fill = factor(educ))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black border
  scale_x_discrete(
    labels = c(
      "1" = "Primary",
      "2" = "Lower Secondary",
      "3" = "Upper Secondary",
      "4" = "Post-Secondary",
      "5" = "Short-Cycle Tertiary",
      "6" = "Bachelor's",
      "7" = "Master's",
      "8" = "Doctoral"
    )
  ) +
  scale_fill_brewer(palette = "RdBu", guide = "none") + 
  labs(
    title = "Health Decline in 2 Years by Educational Level",
    subtitle = "Boxplot of Health Decline Across Education Levels",
    x = "Educational Level",
    y = "Health Decline",
    fill = "Educational Level"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 12, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

#Save Graph
ggsave("educ_health_decline.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for worr_health_dummy per educ:
ggplot(main_educ %>% filter(educ != 0), aes(x = factor(educ), y = worr_health_dummy, fill = factor(educ))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black borders
  scale_x_discrete(
    labels = c(
      "1" = "Primary",
      "2" = "Lower Secondary",
      "3" = "Upper Secondary",
      "4" = "Post-Secondary",
      "5" = "Short-Cycle Tertiary",
      "6" = "Bachelor's",
      "7" = "Master's",
      "8" = "Doctoral"
    )
  ) +
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Health Worries by Educational Level",
    subtitle = "Boxplot of Health Worries Across Education Levels",
    x = "Educational Level",
    y = "Health Worries",
    fill = "Educational Level"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 12, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

#Save Graph
ggsave("educ_worr_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_satisfaction per educ: 
ggplot(main_educ %>% filter(educ != 0), aes(x = factor(educ), y = health_satisfaction, fill = factor(educ))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black border
  scale_x_discrete(
    labels = c(
      "1" = "Primary",
      "2" = "Lower Secondary",
      "3" = "Upper Secondary",
      "4" = "Post-Secondary",
      "5" = "Short-Cycle Tertiary",
      "6" = "Bachelor's",
      "7" = "Master's",
      "8" = "Doctoral"
    )
  ) +
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Health Satisfaction by Educational Level",
    subtitle = "Boxplot of Health Satisfaction Across Education Levels",
    x = "Educational Level",
    y = "Health Satisfaction",
    fill = "Educational Level"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

#Save Graph
ggsave("educ_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

Our dataset mostly contains individuals with upper secondary education levels, with only a few primary school level and doctoral level. We expect those 2 groups to have a high variance.

In all graphs, we notice the same results: positive health perception as well as health satisfaction increases with education, and negative health perception through worrying or health decline decreases with education. We expect education to be correlated with income: people with higher education levels get higher salaries so the effects might be linked.

Income Level Disparities

There are 3 individuals with income over 40k, we will be dropping them for the visualisations as they skew them a lot.

# Aggregate data to calculate mean net income for each pid
cleaned_main <- main %>%
  group_by(pid) %>%
  summarize(net_income = mean(net_income, na.rm = TRUE), .groups = "drop") %>%
  filter(net_income <= 40000) # Remove rows where mean income > 40000

# Distribution of income variable
ggplot(cleaned_main, aes(x = net_income)) +
  geom_histogram(binwidth = 500, fill = "#163E64", color = "black", alpha = 0.7) +  # Use dark blue fill and black borders
  labs(
    title = "Histogram of Net Income Distribution",
    subtitle = "Distribution of Net Income Across Individuals",
    x = "Net Income",
    y = "Count"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 12, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space on the right and top/bottom
  )

ggsave("income.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Group data by pid and educ, and summarize
income_data <- main %>%
  filter(net_income < 40000) %>%
  group_by(pid, net_income) %>%
  summarize(
    health = mean(health, na.rm = TRUE),
    health_decline_2yrs = mean(health_decline_2yrs, na.rm = TRUE),
    worr_health_dummy = mean(worr_health_dummy, na.rm = TRUE),
    health_satisfaction = mean(health_satisfaction, na.rm = TRUE),
    .groups = "drop"
  )

# Health  per Income: 
ggplot(income_data, aes(x = net_income, y = health)) +
    geom_smooth(
    aes(group = 1),  # Ensure a single LOESS line for all bins
    method = "loess",
    color = "#F00000",  # Red for LOESS line
    size = 1.2,  
    se = FALSE, # No confidence interval shading
    span = 1 
  ) +
  stat_summary_bin(fun = "mean", bins = 30, geom = "point", color = "#163E64", size = 2) +  
  labs(
    title = "Health vs. Income (Binned Scatter Plot)",
    x = "Net Income",
    y = "Average Health"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space on the right and top/bottom
  )

## `geom_smooth()` using formula = 'y ~ x'

ggsave("income_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image
## `geom_smooth()` using formula = 'y ~ x'

# Graph for health_decline_2yrs per income: 
income_data <- income_data %>%
  mutate(net_income_bin = cut(net_income, breaks = 10)) # Create income bins
# Reformat income bins into clear labels
income_data <- income_data %>%
  mutate(
    net_income_bin = cut(
      net_income, 
      breaks = 10, 
      labels = c(
        "< 2.5K", 
        "2.5K - 5K", 
        "5K - 7.5K", 
        "7.5K - 10K", 
        "10K - 12.5K", 
        "12.5K - 15K", 
        "15K - 17.5K", 
        "17.5K - 20K", 
        "20K - 22.5K", 
        "> 22.5K"
      )
    )
  )

ggplot(income_data, aes(x = net_income_bin, y = health_decline_2yrs, fill = net_income_bin)) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black border
  scale_fill_brewer(palette = "RdBu", guide = "none") + 
  labs(
    title = "Health Decline by Income (Binned)",
    x = "Net Income (Binned)",
    y = "Health Decline"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("income_health_decline.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for worr_health_dummy per income:
ggplot(income_data, aes(x = worr_health_dummy, fill = net_income_bin)) +
  geom_density(alpha = 0.5, color = "black", size = 0.5) +  # Add transparency and black outline
  scale_fill_brewer(palette = "RdBu", name = "Net Income (Binned)") +
  labs(
    title = "Density of Health Worries by Income",
    x = "Health Worries",
    y = "Density"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "right",  # Move legend to the top
    legend.text = element_text(size = 10, color = "#1E2B4F"),  # Dark blue legend text
    legend.title = element_text(size = 12, face = "bold", color = "#1E2B4F")  # Bold and dark blue legend title
  )

ggsave("income_worr_health.png", plot = last_plot(), dpi = 300)

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# Group data by income bins and calculate average health satisfaction
heatmap_data <- income_data %>%
  mutate(net_income_bin = cut(
    net_income, 
    breaks = 10, 
    labels = c(
      "< 2.5K", 
      "2.5K - 5K", 
      "5K - 7.5K", 
      "7.5K - 10K", 
      "10K - 12.5K", 
      "12.5K - 15K", 
      "15K - 17.5K", 
      "17.5K - 20K", 
      "20K - 22.5K", 
      "> 22.5K"
    )
  )) %>%
  group_by(net_income_bin) %>%
  summarize(avg_health_satisfaction = mean(health_satisfaction, na.rm = TRUE), .groups = "drop")

# Create the heatmap
ggplot(heatmap_data, aes(x = net_income_bin, y = 1, fill = avg_health_satisfaction)) +
  geom_tile(color = "white") +  # Add white borders for separation
  scale_fill_gradient2(
    low = "#67001F",  # Deep Red
    mid = "#F7F7F7",  # Neutral White
    high = "#053061", # Deep Blue
    midpoint = mean(heatmap_data$avg_health_satisfaction, na.rm = TRUE)  # Center the gradient around the mean
  ) +
  labs(
    title = "Average Health Satisfaction by Income Group",
    x = "Net Income (Binned)",
    y = "Health Satisfaction",
    fill = ""
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_blank(),  # Remove y-axis labels (since it’s a single-row heatmap)
    axis.ticks.y = element_blank(),  # Remove y-axis ticks
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"), 

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 70, b = 20, l = 50),  # Add more space around the plot
    
    # Legend styling
    legend.position = "right",  # Move legend to the top
  )

ggsave("income_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

Most of the participants in this dataset have a net income lower than 5000 euros and we see that for those, the higher the income, the higher the average health as we have a positively sloped line. However, for people with higher than 5000 euros income, we see a high variance, with some outliers therefore the negative trend cannot be confirmed.

Box Plot of Net Income by Education Level

ggplot(main, aes(x = factor(educ), y = net_income, fill = factor(educ))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +
  scale_x_discrete(
    labels = c(
      "1" = "Primary",
      "2" = "Lower Secondary",
      "3" = "Upper Secondary",
      "4" = "Post-Secondary",
      "5" = "Short-Cycle Tertiary",
      "6" = "Bachelor's",
      "7" = "Master's",
      "8" = "Doctoral"
    )
  ) +
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Net Income by Education Level",
    x = "Education Level",
    y = "Net Income",
    fill = "Education Level"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space on the right and top/bottom
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("income_educ.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

There is not a significant relationship between education level and net income.

Age Disparities

# Distribution of age variable
ggplot(main, aes(x = age)) +
  geom_histogram(aes(y = after_stat(density)), binwidth = 5, fill = "#A6CEE3", color = "black", alpha = 0.7) + 
  geom_density(color = "#1E2B4F", size = 1) + 
  labs(
    title = "Combined Histogram and Density Plot of Age Distribution",
    x = "Age",
    y = "Density"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

ggsave("age.png", plot = last_plot(), dpi = 300)

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# Health  per age: 
# Filter and create age groups
age_data <- main %>%
  filter(!is.na(age)) %>%  # Remove NA values in the age column
  mutate(
    age_group = cut(
      age,
      breaks = c(25, 30, 35, 40, 45, 50, 55),  
      include.lowest = TRUE,  # Ensures 25 is included in the first group
      right = TRUE,  # Ensures 55 is included in the last group
      labels = c("[25-30)", "[30-35)", "[35-40)", "[40-45)", "[45-50)", "[50-55]")  # Labels with brackets
    )
  )

ggplot(age_data, aes(x = age_group, fill = age_group)) +
  geom_bar(alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Age Group Distribution",
    x = "Age Group",
    y = "Count"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("age2.png", plot = last_plot(), dpi = 300)

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# Create violin plot for health by 5-year age groups
ggplot(age_data, aes(x = age_group, y = health, fill = age_group)) +
  geom_violin(trim = FALSE, alpha = 0.7, color = "black") +  # Add transparency and black border
  scale_fill_brewer(palette = "RdBu", guide = "none") + 
  labs(
    title = "Distribution of Health by 5-Year Age Groups",
    x = "Age Group",
    y = "Health"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("age_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_decline_2yrs per age: 
ggplot(age_data, aes(x = age_group, fill = factor(health_decline_2yrs))) +
  geom_bar(position = "fill", alpha = 0.7, color = "black") + 
  scale_fill_manual(
    values = c("#A6CEE3", "#1E2B4F"), 
    labels = c("No Decline", "Decline"),
    name = "Health Decline"
  ) +
  labs(
    title = "Proportion of Health Decline by Age Group",
    subtitle = "Stacked Bar Chart Showing Health Decline Across Age Groups",
    x = "Age Group",
    y = "Proportion",
    fill = "Health Decline"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "top",  # Move legend to the top
    legend.text = element_text(size = 12, color = "#1E2B4F"),  # Dark blue legend text
    legend.title = element_text(size = 14, face = "bold", color = "#1E2B4F")  # Bold and dark blue legend title
  )

ggsave("age_health_decline.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for worr_health_dummy per age:
ggplot(age_data, aes(x = age_group, fill = factor(worr_health_dummy))) +
  geom_bar(position = "fill", alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_fill_manual(
    values = c("#A6CEE3", "#1E2B4F"),  
    labels = c("No Worries", "Worries"),
    name = "Health Worry"
  ) +
  labs(
    title = "Proportion of Health Worries by Age Group",
    x = "Age Group",
    y = "Proportion",
    fill = "Health Worry"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "top",  # Move legend to the top
    legend.text = element_text(size = 12, color = "#1E2B4F"),  # Dark blue legend text
    legend.title = element_text(size = 14, face = "bold", color = "#1E2B4F")  # Bold and dark blue legend title
  )

ggsave("age_worr_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_satisfaction per age: 
ggplot(age_data, aes(x = age_group, y = health_satisfaction, fill = age_group)) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black border
  scale_fill_brewer(palette = "RdBu", guide = "none") + 
  labs(
    title = "Health Satisfaction by Age Group",
    x = "Age Group",
    y = "Health Satisfaction"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("age_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

In our dataset, the most participants we have are around the age of 45. For all health variables, we notice the same trend: the positive subjective health perceptions are higher within younger individuals, health worries increases with age, and health satisfaction decreases with age. We also notice that health decline is stable across all age groups at around 24% and health doesn’t largely vary. Because we expect older individuals to have a higher income, we should look into the intersection of age and income and their impact on health.

Scatter Plot of Net Income vs. Age

ggplot(main, aes(x = age, y = net_income)) +
  geom_point(alpha = 0.6, color = "#1E2B4F") + 
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

ggsave("income_age.png", plot = last_plot(), dpi = 300)

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Net income does increase with age but not significantly.

Marital Status Disparities

# Group data by pid and rel_status, and summarize
main_rel <- main %>%
  group_by(pid, rel_status) %>%
  summarize(
    health = mean(health, na.rm = TRUE),
    health_decline_2yrs = mean(health_decline_2yrs, na.rm = TRUE),
    worr_health_dummy = mean(worr_health_dummy, na.rm = TRUE),
    health_satisfaction = mean(health_satisfaction, na.rm = TRUE),
    .groups = "drop"
  )
# Distribution of rel_status variable
ggplot(main_rel, aes(x = factor(rel_status), fill = factor(rel_status))) +
  geom_bar(alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Distribution of Relationship Status",
    x = "Relationship Status",
    y = "Count"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("rel_status.png", plot = last_plot(), dpi = 300)

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# Health  per rel_status: 

ggplot(main_rel, aes(x = factor(rel_status), y = health, fill = factor(rel_status))) +
  geom_bar(stat = "summary", fun = "mean", alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Average Health by Relationship Status",
    x = "Relationship Status",
    y = "Average Health"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("rel_status_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_decline_2yrs per rel_status: 
ggplot(main_rel, aes(x = factor(rel_status), y = health_decline_2yrs, fill = factor(rel_status))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black border
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Health Decline by Relationship Status",
    x = "Relationship Status",
    y = "Health Decline"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("rel_status_health_decline.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for worr_health_dummy per rel_status:
ggplot(main_rel, aes(x = factor(rel_status), y = worr_health_dummy, fill = factor(rel_status))) +
  geom_bar(stat = "summary", fun = "mean", alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_fill_brewer(palette ="RdBu", guide = "none") + 
  labs(
    title = "Average Health Worries by Relationship Status",
    x = "Relationship Status",
    y = "Average Health Worries"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 50, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("rel_status_worr_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_satisfaction per rel_status: 
ggplot(main_rel, aes(x = factor(rel_status), y = health_satisfaction, fill = factor(rel_status))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black borders
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  labs(
    title = "Health Satisfaction by Relationship Status",
    x = "Relationship Status",
    y = "Health Satisfaction"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("rel_status_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

Our dataset contains mostly married individuals, which makes sense as our main population is around the age of 45. Average health is quite consistent across all relationship statuses, as well as health decline and health satisfaction. It is different for separated individuals and those with spouses abroad but the low number of these observations causing high variance does not allow us to make conclusions.

We notice that single individuals are the least worried about their health but we expect this to be caused by the younger age of single participants. We will therefore examine the relationship between marital status and age.

Box Plot of Age by Relationship Status

ggplot(main, aes(x = factor(rel_status), y = age, fill = factor(rel_status))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +
  scale_x_discrete(
    labels = c(
      "1" = "Single",
      "2" = "Married",
      "3" = "Divorced",
      "4" = "Widowed"
    )
  ) +
  scale_fill_brewer(palette = "RdBu", guide = "none") + 
  labs(
    title = "Age by Relationship Status",
    x = "Relationship Status",
    y = "Age"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("rel_status_age.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

As expected, the single group is younger but this is not significant as the variance is quite high.

Disparities by Place of Birth

# Group data by pid and germborn, and summarize
main_germborn <- main %>%
  group_by(pid, germborn) %>%
  summarize(
    health = mean(health, na.rm = TRUE),
    health_decline_2yrs = mean(health_decline_2yrs, na.rm = TRUE),
    worr_health_dummy = mean(worr_health_dummy, na.rm = TRUE),
    health_satisfaction = mean(health_satisfaction, na.rm = TRUE),
    .groups = "drop"
  )
# Distribution of germborn variable
ggplot(main_germborn, aes(x = factor(germborn), fill = factor(germborn))) +
  geom_bar(alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_x_discrete(
    labels = c(
      "0" = "Born outside Germany", 
      "1" = "Born in Germany"
    )
  ) +
  scale_fill_manual(
    values = c("#A6CEE3", "#1E2B4F"), 
    guide = "none"  # Remove legend
  ) +
  labs(
    title = "Distribution of German-Born Individuals",
    x = "Migration Status",
    y = "Count"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

ggsave("germborn.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Health per germborn: 
ggplot(main_germborn, aes(x = factor(germborn), y = health, fill = factor(germborn))) +
  geom_violin(trim = FALSE, alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_fill_manual(
    values = c("#A6CEE3", "#1E2B4F"),  # Light blue and dark blue
    labels = c("Born Outside of Germany", "Born in Germany"),
    name = "German-Born Status"
  ) +
  scale_x_discrete(
    labels = c(
      "0" = "Born Outside of Germany",
      "1" = "Born in Germany"
    )
  ) +
  labs(
    title = "Distribution of Health by Migration Status",
    x = "",
    y = "Health"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("germborn_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_decline_2yrs per germborn: 
ggplot(main_germborn, aes(x = factor(germborn), y = health_decline_2yrs, fill = factor(germborn))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black borders
  scale_fill_manual(
    values = c("#A6CEE3", "#1E2B4F"),  # Light blue and dark blue
    labels = c("Born Outside of Germany", "Born in Germany"),
    name = "Migration Status"
  ) +
  scale_x_discrete(
    labels = c(
      "0" = "Born Outside of Germany",
      "1" = "Born in Germany"
    )
  ) +
  labs(
    title = "Health Decline by Migration Status",
    x = "",
    y = "Health Decline"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F", hjust = 0.5),  # Centered and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("germborn_health_decline.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for worr_health_dummy per germborn:
ggplot(main_germborn, aes(x = worr_health_dummy, fill = factor(germborn))) +
  geom_density(alpha = 0.5, color = "black") +  # Add transparency and black outline for density curves
  scale_fill_manual(
    values = c("#F00000", "#1E2B4F"), 
    labels = c("Born Outside of Germany", "Born in Germany"),
    name = "Migration Status"
  ) +
  labs(
    title = "Density of Health Worries by Migration Status",
    x = "Health Worries",
    y = "Density"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "top",  # Place legend at the top
    legend.text = element_text(size = 12, color = "#1E2B4F"),  # Dark blue legend text
    legend.title = element_text(size = 14, face = "bold", color = "#1E2B4F")  # Bold and dark blue legend title
  )

ggsave("germborn_worr_health.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# Graph for health_satisfaction per germborn: 
ggplot(main_germborn, aes(x = factor(germborn), y = health_satisfaction, fill = factor(germborn))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black borders
  scale_fill_manual(
    values = c("#A6CEE3", "#1E2B4F"),  # Light blue and dark blue
    labels = c("Born Outside of Germany", "Born in Germany"),
    name = "Migration Status"
  ) +
  scale_x_discrete(
    labels = c(
      "0" = "Born Outside of Germany",
      "1" = "Born in Germany"
    )
  ) +
  labs(
    title = "Health Satisfaction by Migration Status",
    x = "",
    y = "Health Satisfaction"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F", hjust = 0.5),  # Bold and centered dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("germborn_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

Our dataset mostly contains individuals born in Germany, which makes sense as it is the SOEP data. For people born in Germany or Outside of Germany, health distributions are quite similar. We do notice that individuals born outside of Germany have smaller health declines but also higher health worries and lower health satisfaction. The small differences, the contradictory findings, merged with the fact that we only have a small sample of individuals born outside of Germany does not allow us to make conclusion.

Relationship between subjective and objective health

# worr_health_categorical per health_satisfaction: 
ggplot(main, aes(x = factor(worr_health_categorical), y = health_satisfaction, fill = factor(worr_health_categorical))) +
  geom_boxplot(alpha = 0.7, outlier.shape = 16, outlier.size = 2, color = "black") +  # Add transparency and black borders
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  scale_x_discrete(
    labels = c(
      "1" = "Does Not Worry",
      "2" = "Worries a Little",
      "3" = "Worries a Lot"
    )
  ) +
  labs(
    title = "Health Satisfaction by Health Worry Categories",
    x = "Health Worry Category",
    y = "Health Satisfaction"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("worr_health_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# health_satisfaction per life_satisfaction: 
ggplot(main, aes(x = life_satisfaction, y = health_satisfaction)) +
  geom_bin2d(bins = 30) +
  scale_fill_gradient(
    low = "#A6CEE3",  # Light blue
    high = "#1E2B4F", # Dark blue
    name = "Count"    # Legend title
  ) +
  labs(
    title = "Health Satisfaction vs. Life Satisfaction",
    x = "Life Satisfaction",
    y = "Health Satisfaction"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "right",  # Position legend on the right
    legend.text = element_text(size = 12, color = "#1E2B4F"),  # Dark blue legend text
    legend.title = element_text(size = 14, face = "bold", color = "#1E2B4F")  # Bold and dark blue legend title
  )

ggsave("life_health_satisfaction.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

# health per BMI graph: 
ggplot(main, aes(x = factor(bmi_categorical), y = health, fill = factor(bmi_categorical))) +
  geom_violin(trim = FALSE, alpha = 0.7, color = "black") +  # Add transparency and black borders
  scale_fill_brewer(palette = "RdBu", guide = "none") +  
  scale_x_discrete(
    labels = c(
      "1" = "Underweight",
      "2" = "Normal Weight",
      "3" = "Overweight",
      "4" = "Obese"
    )
  ) +
  labs(
    title = "Health Distribution by BMI Category",
    x = "BMI Category",
    y = "Health"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, angle = 45, hjust = 1, face = "bold", color = "#1E2B4F"),  # Tilted and bold dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Legend styling
    legend.position = "none"  # Remove legend
  )

ggsave("health_bmi.png", plot = last_plot(), dpi = 300)

## Saving 7 x 5 in image

Further analyses to confirm our expectations, we see that the higher the health satisfaction, the lower the individuals worry about their health and that goes both ways.

Similarly, the higher life satisfaction, the higher health satisfaction as we observe a linear increasing relationship between the two.

Analyzing BMI, we also see that normal and overweight individuals show higher health. However, due to the low amount of observations of underweight and obese individuals, we cannot make conclusions.

Prep for Analysis

Create new dummys

In this section, we create new dummies for university degree, being married or not, having a white collar job or being self-employed. Our research led us to find literature that highlighted these categories as significant when it comes to subjective and objective health, therefore we will include them in our models.

# Create university_dummy (university-level education: educ = 6, 7, 8)
main <- main %>%
  mutate(university_dummy = ifelse(educ %in% c(6, 7, 8), 1, 0))

# Create married_dummy (married status: rel_status = "married")
main <- main %>%
  mutate(married_dummy = ifelse(rel_status == "married", 1, 0))

# Create white_collar_dummy and self_employed_dummy from occupational_status
main <- main %>%
  mutate(
    white_collar_dummy = ifelse(occup_status %in% c("White Collar - Self-Employed", "White Collar Employee"), 1, 0),
    self_employed_dummy = ifelse(occup_status %in% c("White Collar - Self-Employed", "Agriculture - Self-Employed"), 1, 0)
  )

Visualise new dummies

# Select the dummy variables to visualize
dummy_data <- main %>%
  select(university_dummy, married_dummy, white_collar_dummy, self_employed_dummy) %>%
  pivot_longer(cols = everything(), names_to = "DummyVariable", values_to = "Value") %>%
  group_by(DummyVariable, Value) %>%
  summarise(Count = n(), .groups = "drop")

# Create a bar plot for the distribution of each dummy variable
ggplot(dummy_data, aes(x = as.factor(Value), y = Count, fill = as.factor(Value))) +
  geom_bar(stat = "identity", color = "black") +  # Add black borders to the bars
  facet_wrap(~ DummyVariable, scales = "free_y") +  # Facet by DummyVariable with free y-scales
  labs(
    title = "Distribution of Dummy Variables",
    x = "Dummy Value (0 = No, 1 = Yes)",
    y = "Count"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#1E2B4F")  # Red for "No" (0) and dark blue for "Yes" (1)
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis text
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title

    # Facet styling
    strip.background = element_rect(fill = "white", color = NA),  
    strip.text = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Dark blue facet labels
    
    # Remove legend
    legend.position = "none"  
  )

Summary Statistics

Detailed Summary Statistics Tables

# Define health group labels and titles
main <- main %>%
  mutate(
    health_group = case_when(
      health >= 1 & health <= 2 ~ "1-2",
      health > 2 & health <= 3 ~ "2-3",
      health > 3 & health <= 5 ~ "4-5",
      TRUE ~ NA_character_
    )
  )

health_titles <- c(
  "1-2" = "Poor health",
  "2-3" = "Moderate health",
  "4-5" = "Good health"
)

# Function to calculate summary statistics for a variable
calculate_group_summary <- function(data, var_name, var_label) {
  data %>%
    summarise(
      Mean = mean(!!sym(var_name), na.rm = TRUE),
      SD = sd(!!sym(var_name), na.rm = TRUE),
      Min = min(!!sym(var_name), na.rm = TRUE),
      Max = max(!!sym(var_name), na.rm = TRUE),
      Count = n()
    ) %>%
    mutate(Variable = var_label)
}

# Variables to calculate statistics for
variables <- list(
  list(name = "BMI", label = "BMI"),
  list(name = "worr_health_dummy", label = "Worries About Health (Dummy)"),
  list(name = "smoking_dummy", label = "Smoking (Dummy)"),
  list(name = "health_in_2yrs", label = "Health in 2 Years"),
  list(name = "health_decline_2yrs", label = "Expected Health Decline in 2 Years"),
  list(name = "life_satisfaction", label = "Life Satisfaction"),
  list(name = "health_satisfaction", label = "Health Satisfaction"),
  list(name = "tenure", label = "Tenure"),
  list(name = "net_income", label = "Net Income"),
  list(name = "work_time_weekly", label = "Work Time Weekly"),
  list(name = "total_years_unemployment", label = "Total Years Unemployment"),
  list(name = "worr_job_dummy", label = "Job Worries (Dummy)"),
  list(name = "worr_financial_dummy", label = "Financial Worries (Dummy)"),
  list(name = "worr_economic_dummy", label = "Economic Worries (Dummy)"),
  list(name = "male", label = "Gender (Male = 1)"),
  list(name = "age", label = "Age"),
  list(name = "university_dummy", label = "University (Dummy)"),
  list(name = "married_dummy", label = "Married (Dummy)"),
  list(name = "white_collar_dummy", label = "White Collar Job (Dummy)"),
  list(name = "self_employed_dummy", label = "Self Employed (Dummy)")
)

# Initialize a list to store tables for each group
group_tables <- list()

# Generate separate tables for each health group
for (group in unique(main$health_group)) {
  group_data <- main %>% filter(health_group == group)
  group_table <- data.frame(
    Variable = character(),
    Mean = numeric(),
    SD = numeric(),
    Min = numeric(),
    Max = numeric(),
    Count = numeric(),
    stringsAsFactors = FALSE
  )
  
  for (var in variables) {
    stats <- calculate_group_summary(group_data, var$name, var$label)
    if (!is.null(stats)) {
      group_table <- bind_rows(group_table, stats)
    }
  }
  
  # Round all numeric columns to 1 digit after the decimal point
  group_table <- group_table %>%
    mutate(
      Mean = round(Mean, 1),
      SD = round(SD, 1),
      Min = round(Min, 1),
      Max = round(Max, 1)
    )
  
  # Add the table to the list with the title as the key
  table_title <- health_titles[group]
  group_tables[[table_title]] <- group_table
}

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

## Warning: `..1$Min` and `..2$Min` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Min`.
## ✖ Values: -7 and -3

## Warning: `..1$Max` and `..2$Max` have conflicting value labels.
## ℹ Labels for these values will be taken from `..1$Max`.
## ✖ Values: -7 and -3

# Display each group's table with its title
for (title in names(group_tables)) {
  print(paste("Summary statistics for:", title))
  print(group_tables[[title]])
}

## [1] "Summary statistics for: Poor health"
##                              Variable   Mean     SD Min     Max Count
## 1                                 BMI   27.9    6.7  12   163.6  9006
## 2        Worries About Health (Dummy)    1.0    0.2   0     1.0  9006
## 3                     Smoking (Dummy)    0.5    0.5   0     1.0  9006
## 4                   Health in 2 Years    2.6    0.9   1     5.0  9006
## 5  Expected Health Decline in 2 Years    0.1    0.2   0     1.0  9006
## 6                   Life Satisfaction    5.7    2.1   0    10.0  9006
## 7                 Health Satisfaction    3.8    1.9   0    10.0  9006
## 8                              Tenure    6.9    8.9   0    40.9  9006
## 9                          Net Income 1069.2 1187.2   0 15000.0  9006
## 10                   Work Time Weekly   24.8   20.5   0    80.0  9006
## 11           Total Years Unemployment    2.1    3.9   0    29.0  9006
## 12                Job Worries (Dummy)    0.4    0.5   0     1.0  9006
## 13          Financial Worries (Dummy)    0.9    0.4   0     1.0  9006
## 14           Economic Worries (Dummy)    0.9    0.4   0     1.0  9006
## 15                  Gender (Male = 1)    0.4    0.5   0     1.0  9006
## 16                                Age   43.4    7.8  25    55.0  9006
## 17                 University (Dummy)    0.2    0.4   0     1.0  9006
## 18                    Married (Dummy)    0.6    0.5   0     1.0  9006
## 19           White Collar Job (Dummy)    0.4    0.5   0     1.0  9006
## 20              Self Employed (Dummy)    0.1    0.2   0     1.0  9006
## [1] "Summary statistics for: Moderate health"
##                              Variable   Mean     SD  Min      Max Count
## 1                                 BMI   26.8    5.3 12.9    128.5 21384
## 2        Worries About Health (Dummy)    0.9    0.4  0.0      1.0 21384
## 3                     Smoking (Dummy)    0.4    0.5  0.0      1.0 21384
## 4                   Health in 2 Years    3.2    0.8  1.0      5.0 21384
## 5  Expected Health Decline in 2 Years    0.2    0.4  0.0      1.0 21384
## 6                   Life Satisfaction    6.8    1.6  0.0     10.0 21384
## 7                 Health Satisfaction    6.1    1.5  0.0     10.0 21384
## 8                              Tenure    8.6    9.0  0.0     40.1 21384
## 9                          Net Income 1425.6 1566.4  0.0 124219.0 21384
## 10                   Work Time Weekly   31.2   18.5  0.0     80.0 21384
## 11           Total Years Unemployment    1.2    2.7  0.0     37.0 21384
## 12                Job Worries (Dummy)    0.5    0.5  0.0      1.0 21384
## 13          Financial Worries (Dummy)    0.8    0.4  0.0      1.0 21384
## 14           Economic Worries (Dummy)    0.9    0.4  0.0      1.0 21384
## 15                  Gender (Male = 1)    0.5    0.5  0.0      1.0 21384
## 16                                Age   42.3    7.9 25.0     55.0 21384
## 17                 University (Dummy)    0.2    0.4  0.0      1.0 21384
## 18                    Married (Dummy)    0.6    0.5  0.0      1.0 21384
## 19           White Collar Job (Dummy)    0.5    0.5  0.0      1.0 21384
## 20              Self Employed (Dummy)    0.1    0.3  0.0      1.0 21384
## [1] "Summary statistics for: Good health"
##                              Variable   Mean     SD  Min     Max Count
## 1                                 BMI   25.3    4.5 12.6   197.2 43936
## 2        Worries About Health (Dummy)    0.5    0.5  0.0     1.0 43936
## 3                     Smoking (Dummy)    0.3    0.5  0.0     1.0 43936
## 4                   Health in 2 Years    3.9    0.7  1.0     5.0 43936
## 5  Expected Health Decline in 2 Years    0.3    0.5  0.0     1.0 43936
## 6                   Life Satisfaction    7.8    1.3  0.0    10.0 43936
## 7                 Health Satisfaction    8.1    1.3  0.0    10.0 43936
## 8                              Tenure    7.8    8.3  0.0    40.0 43936
## 9                          Net Income 1583.5 1500.6  0.0 99999.0 43936
## 10                   Work Time Weekly   32.1   17.9  0.0    80.0 43936
## 11           Total Years Unemployment    0.7    1.9  0.0    27.6 43936
## 12                Job Worries (Dummy)    0.4    0.5  0.0     1.0 43936
## 13          Financial Worries (Dummy)    0.7    0.5  0.0     1.0 43936
## 14           Economic Worries (Dummy)    0.8    0.4  0.0     1.0 43936
## 15                  Gender (Male = 1)    0.5    0.5  0.0     1.0 43936
## 16                                Age   39.9    8.1 25.0    55.0 43936
## 17                 University (Dummy)    0.3    0.5  0.0     1.0 43936
## 18                    Married (Dummy)    0.6    0.5  0.0     1.0 43936
## 19           White Collar Job (Dummy)    0.6    0.5  0.0     1.0 43936
## 20              Self Employed (Dummy)    0.1    0.3  0.0     1.0 43936

# Save each group's table to separate CSV files
for (title in names(group_tables)) {
  write.csv(group_tables[[title]], paste0("summary_table_", gsub(" ", "_", title), ".csv"), row.names = FALSE)
}

Short Summary Statistics Table

# Define health group labels and titles
main <- main %>%
  mutate(
    health_group = case_when(
      health >= 1 & health <= 2 ~ "1-2",
      health > 2 & health <= 3 ~ "3",
      health > 3 & health <= 5 ~ "4-5",
      TRUE ~ NA_character_
    )
  )

health_titles <- c(
  "1-2" = "Poor health",
  "3" = "Moderate health",
  "4-5" = "Good health"
)

# Variables to calculate statistics for
variables <- list(
list(name = "BMI", label = "BMI"),
  list(name = "worr_health_dummy", label = "Worries About Health (Dummy)"),
  list(name = "smoking_dummy", label = "Smoking (Dummy)"),
  list(name = "health_in_2yrs", label = "Health in 2 Years"),
  list(name = "health_decline_2yrs", label = "Expected Health Decline in 2 Years"),
  list(name = "life_satisfaction", label = "Life Satisfaction"),
  list(name = "health_satisfaction", label = "Health Satisfaction"),
  list(name = "tenure", label = "Tenure"),
  list(name = "net_income", label = "Net Income"),
  list(name = "work_time_weekly", label = "Work Time Weekly"),
  list(name = "total_years_unemployment", label = "Total Years Unemployment"),
  list(name = "worr_job_dummy", label = "Job Worries (Dummy)"),
  list(name = "worr_financial_dummy", label = "Financial Worries (Dummy)"),
  list(name = "worr_economic_dummy", label = "Economic Worries (Dummy)"),
  list(name = "male", label = "Gender (Male = 1)"),
  list(name = "age", label = "Age"),
  list(name = "university_dummy", label = "University (Dummy)"),
  list(name = "married_dummy", label = "Married (Dummy)"),
  list(name = "white_collar_dummy", label = "White Collar Job (Dummy)"),
  list(name = "self_employed_dummy", label = "Self Employed (Dummy)")
)

# Create a summary table
summary_table <- data.frame(Variable = sapply(variables, function(x) x$label))

# Calculate means for each health category
for (group in unique(main$health_group)) {
  group_data <- main %>% filter(health_group == group)
  group_means <- sapply(variables, function(var) mean(group_data[[var$name]], na.rm = TRUE))
  summary_table[[health_titles[group]]] <- round(group_means, 1)
}

# Add row for the number of observations in each health category
num_observations <- sapply(unique(main$health_group), function(group) nrow(main %>% filter(health_group == group)))
summary_table <- rbind(summary_table, c("Number of Observations", num_observations))

# Display the summary table
print(summary_table)

##                              Variable Poor health Moderate health Good health
## 1                                 BMI        27.9            26.8        25.3
## 2        Worries About Health (Dummy)           1             0.9         0.5
## 3                     Smoking (Dummy)         0.5             0.4         0.3
## 4                   Health in 2 Years         2.6             3.2         3.9
## 5  Expected Health Decline in 2 Years         0.1             0.2         0.3
## 6                   Life Satisfaction         5.7             6.8         7.8
## 7                 Health Satisfaction         3.8             6.1         8.1
## 8                              Tenure         6.9             8.6         7.8
## 9                          Net Income      1069.2          1425.6      1583.5
## 10                   Work Time Weekly        24.8            31.2        32.1
## 11           Total Years Unemployment         2.1             1.2         0.7
## 12                Job Worries (Dummy)         0.4             0.5         0.4
## 13          Financial Worries (Dummy)         0.9             0.8         0.7
## 14           Economic Worries (Dummy)         0.9             0.9         0.8
## 15                  Gender (Male = 1)         0.4             0.5         0.5
## 16                                Age        43.4            42.3        39.9
## 17                 University (Dummy)         0.2             0.2         0.3
## 18                    Married (Dummy)         0.6             0.6         0.6
## 19           White Collar Job (Dummy)         0.4             0.5         0.6
## 20              Self Employed (Dummy)         0.1             0.1         0.1
## 21             Number of Observations        9006           21384       43936

# Save the summary table as a CSV file
write.csv(summary_table, "summary_table_short.csv", row.names = FALSE)

The table provides descriptive statistics for individuals categorized by their self-reported health status: Good health, Moderate health, and Poor health. Each variable is summarized for these three health categories, allowing us to analyze how different characteristics vary across health statuses. - BMI Individuals with poorer health tend to have higher BMI (Good: 25.3 → Poor: 27.8), suggesting a link between obesity and poorer health. - Worries About Health (Dummy) Health worries increase with poorer health (Good: 0.5 → Poor: 1.0), as expected. - Individuals in poorer health have significantly lower expectations of good health in the future (Good: 3.9 → Poor: 2.6), also as expected. - Similarly, individuals in Poor health report much lower health satisfaction (Good: 8.1 → Poor: 3.8) and a decline in life satisfaction as health worsens (Good: 7.8 → Poor: 5.7). - Higher unemployment duration is associated with poorer health (Good: 0.7 years → Poor: 2.1 years). - Worries about finances and the economy increase slightly as health worsens. - Individuals in Good health have significantly higher incomes (Good: €1574 → Poor: €1060). - Poor health correlates with increasing age (Good: 39.8 → Poor: 43.3). - People who do go to University have slightly better health (Good: 0.3 → Poor: 0.2). Lower education might contribute to worse health outcomes. - Surprisingly, those in poorer health report less expected decline (Good: 0.3 → Poor: 0.1). This could indicate resignation or lower health awareness.

But, in general, in our dataset, most individuals report Good health (45,372), with fewer in Moderate health (21,859) and the least in Poor health (9,276). This indicates a skewed distribution towards better health.

Modelling

Lasso Classification: Health worries as an outcome Variable

# Convert data to panel format
panel_data <- pdata.frame(main, index = c("pid", "syear"))  # pid = individual ID, syear = time

# Prepare data for LASSO regression
lasso_data <- panel_data %>%
  dplyr::select(
    pid, syear, health_decline_2yrs, health_in_2yrs, worr_health_dummy, health, BMI, smoking_dummy, life_satisfaction, health_satisfaction,
    tenure, net_income, work_time_weekly, total_years_unemployment, 
    worr_job_dummy, worr_financial_dummy, worr_economic_dummy,
    male, age, university_dummy, married_dummy, white_collar_dummy, self_employed_dummy
  ) %>%
  na.omit()  # Remove missing values

# Check class distribution in y
class_distribution <- table(lasso_data$worr_health_dummy)
print(class_distribution)

## 
##     0     1 
## 25812 48514

# Split the data into training and test data
set.seed(12345) # For reproducibility
trainIndex <- createDataPartition(lasso_data$worr_health_dummy, p = 0.7, list = FALSE)
# Convert trainIndex to a vector
trainIndex <- as.vector(trainIndex)
# Use the vector to split the data
trainData <- lasso_data[trainIndex, ]
testData <- lasso_data[-trainIndex, ]

# Standardize numerical variables
# Define relevant numerical variables as a character vector
numerical_vars <- c(
  "BMI", "smoking_dummy", "life_satisfaction", "health_satisfaction",
  "tenure", "net_income", "work_time_weekly", "total_years_unemployment",
  "worr_job_dummy", "worr_financial_dummy", "worr_economic_dummy",
  "male", "age", "health", "married_dummy","university_dummy","self_employed_dummy","white_collar_dummy"
)

# Apply pre-processing (center and scale) only to the selected numerical columns
preProcValues <- preProcess(trainData[, numerical_vars], method = c("center", "scale"))

# Standardize the training data
trainData[, numerical_vars] <- predict(preProcValues, trainData[, numerical_vars])

# Standardize the test data
testData[, numerical_vars] <- predict(preProcValues, testData[, numerical_vars])

# Exclude pid and syear and -health_in_2yrs and -health_decline_in_2yrs to avoid overfitting
trainData <- trainData %>% select(-pid, -syear, -health_in_2yrs, -health_decline_2yrs)
testData <- testData %>% select(-pid, -syear, -health_in_2yrs, -health_decline_2yrs)


# Convert worr_health_dummy to a factor
trainData$worr_health_dummy <- factor(trainData$worr_health_dummy, levels = c(0, 1), labels = c("No", "Yes"))
testData$worr_health_dummy <- factor(testData$worr_health_dummy, levels = c(0, 1), labels = c("No", "Yes"))

# Set up the training control
train_control <- trainControl(method = "cv", number = 10, classProbs = TRUE, summaryFunction = twoClassSummary)

# Train the LASSO model for classification
set.seed(12345)
lasso_model <- train(
  worr_health_dummy ~ .,  
  data = trainData,
  method = "glmnet",        # Specify LASSO
  family = "binomial",      # Classification for binary outcome
  trControl = train_control,  # Use predefined training control
  tuneGrid = expand.grid(alpha = 1, lambda = seq(0.001, 0.5, by = 0.001)), # LASSO tuning grid
  metric = "ROC"  # Use ROC as the evaluation metric
)

# Display the best lambda value and model summary
print(lasso_model$bestTune)

##   alpha lambda
## 1     1  0.001

# Visualize the cross-validation results
plot(lasso_model)

# Extract the cross-validation results
cv_results <- lasso_model$results

# Model Evaluation
# Predict probabilities on the test set
predictions <- predict(lasso_model, newdata = testData, type = "prob")

# Predict binary outcomes (threshold = 0.5)
predicted_classes <- ifelse(predictions[, "Yes"] > 0.5, "Yes", "No")

# Confusion matrix
conf_matrix <- confusionMatrix(factor(predicted_classes, levels = c("No", "Yes")), 
                               factor(testData$worr_health_dummy, levels = c("No", "Yes")))
print(conf_matrix)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    No   Yes
##        No   4360  1970
##        Yes  3399 12568
##                                           
##                Accuracy : 0.7592          
##                  95% CI : (0.7535, 0.7648)
##     No Information Rate : 0.652           
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.4456          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
##                                           
##             Sensitivity : 0.5619          
##             Specificity : 0.8645          
##          Pos Pred Value : 0.6888          
##          Neg Pred Value : 0.7871          
##              Prevalence : 0.3480          
##          Detection Rate : 0.1955          
##    Detection Prevalence : 0.2839          
##       Balanced Accuracy : 0.7132          
##                                           
##        'Positive' Class : No              
##

# Evaluate model performance
print(paste0("Accuracy: ", conf_matrix$overall["Accuracy"]))

## [1] "Accuracy: 0.759205274252142"

print(paste0("Sensitivity: ", conf_matrix$byClass["Sensitivity"]))

## [1] "Sensitivity: 0.561928083515917"

print(paste0("Specificity: ", conf_matrix$byClass["Specificity"]))

## [1] "Specificity: 0.864493052689503"

This LASSO classification model predicts worries about health as a binary outcome (Dummy variable) and provides the following performance metrics:

Accuracy (76%): The model correctly predicts whether an individual is worried about their health in 76% of cases. This suggests that overall, the model performs reasonably well.
Sensitivity (56%): The model correctly identifies 56% of individuals who actually have health worries. This means it has moderate ability to detect those who are worried about their health but may miss some cases (higher false negatives).
Specificity (86%): The model correctly identifies 86% of individuals who do not have health worries, meaning it is quite good at ruling out people who are not worried about their health (lower false positives).

# Convert sparse matrix to data frame and filter non-zero coefficients
coefficients <- coef(lasso_model$finalModel, s = lasso_model$bestTune$lambda)

non_zero_coefficients <- data.frame(
  Variable = rownames(as.matrix(coefficients)),
  Coefficient = as.numeric(as.matrix(coefficients))
) %>%
  filter(Coefficient != 0)  # Keep only non-zero coefficients

# Remove the intercept and rename variables
non_zero_coefficients <- non_zero_coefficients %>%
  filter(Variable != "(Intercept)") %>%  # Remove the intercept
  mutate(
    Variable = case_when(  # Rename variables for cleaner labels
      Variable == "health" ~ "Health",
      Variable == "health_satisfaction" ~ "Health Satisfaction",
      Variable == "life_satisfaction" ~ "Life Satisfaction",
      Variable == "educ" ~ "Education Level",
      Variable == "male" ~ "Gender (Male=1)",
      Variable == "worr_job_dummy" ~ "Job Worries (Dummy)",
      Variable == "tenure" ~ "Tenure",
      Variable == "work_time_weekly" ~ "Work Time Weekly",
      Variable == "net_income" ~ "Net Income",
      Variable == "total_years_unemployment" ~ "Total Years Unemployed",
      Variable == "worr_financial_dummy" ~ "Financial Worries (Dummy)",
      Variable == "smoking_dummy" ~ "Smoking (Dummy)",
      Variable == "worr_health_dummy" ~ "Worries About Health (Dummy)",
      Variable == "worr_economic_dummy" ~ "Worries About the Economy (Dummy)",
      Variable == "BMI" ~ "BMI",
      Variable == "age" ~ "Age",
      Variable == "university_dummy" ~ "University (Dummy)",
      Variable == "married_dummy" ~ "Married (Dummy)",
      Variable == "white_collar_dummy" ~ "White Collar Job (Dummy)",
      Variable == "self_employed_dummy" ~ "Self Employed (Dummy)",
      TRUE ~ Variable 
    )
  )

# Plotting non-zero coefficients with cleaner labels
ggplot(non_zero_coefficients, aes(x = reorder(Variable, Coefficient), y = Coefficient, fill = Coefficient > 0)) +
  geom_bar(stat = "identity", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Non-Zero Coefficients from Lasso Classification",
    x = "",
    y = "Coefficient Value"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#1E2B4F"),  # Red for negative, dark blue for positive
    guide = "none"  # Remove the legend
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_blank(),  # Remove x-axis title
    axis.title.y = element_blank(),  # Remove y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis text

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

#Save Graph
ggsave("lasso_coefficients_classification_health_worries.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

Top Predictors - Worrying about finances: Individuals who worry about their financial situation are more likely to also worry about their health, suggesting a link between economic insecurity and health-related stress. - Worrying about job security: Job-related concerns contribute to health worries, possibly due to stress or uncertainty - about access to healthcare and stability. - Actual health status: Those with worse self-reported health are more prone to worrying about their health, reinforcing the idea that poor health conditions lead to increased concern. - Health satisfaction: Lower satisfaction with one’s health is strongly associated with worrying about health, which aligns with the expectation that dissatisfaction leads to increased concern.

Secondary Predictors - Age: Older individuals may worry more about health, likely due to increased vulnerability to illness. However, the effect is weaker compared to financial and job worries. - BMI (Body Mass Index): Higher BMI may contribute to health worries, possibly reflecting concerns about obesity-related conditions like heart disease or diabetes. - Being male: While gender plays a role, it is a weaker predictor. This could suggest that men worry about health less than women, or that their health worries are driven by different factors.

Evaluating the distribution of our outcome variable: Health in 2 years -categorical-

# Create the bar plot
ggplot(main, aes(x = factor(health_in_2yrs), fill = health_in_2yrs)) +
  geom_bar(color = "black") +  # Add black border for clarity
  scale_fill_distiller(palette = "RdBu", direction = 1) +  # Use RdBu color palette
  labs(
    title = "Distribution of Health in 2 Years",
    x = "Health in 2 Years",
    y = "Count",
    fill = "Health Score"
  ) +
  theme_minimal(base_size = 14) +  # Clean aesthetic
  theme(
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, margin = ggplot2::margin(b = 10)),
    axis.title.x = element_text(size = 14, color = "#1E2B4F"),
    axis.title.y = element_text(size = 14, color = "#1E2B4F"),
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),
    legend.title = element_text(size = 12, face = "bold"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_rect(fill = "white", color = NA)
  )

For most participants, health in 2 years is around 4 or 3.

Lasso Regression: Health in 2 years -categorical- as an outcome Variable

# Convert data to panel format
panel_data <- pdata.frame(main, index = c("pid", "syear"))  # pid = individual ID, syear = time

# Prepare data for LASSO regression
lasso_data <- panel_data %>%
  dplyr::select(
    pid, syear, health_decline_2yrs, health_in_2yrs, worr_health_dummy, health, BMI, smoking_dummy, life_satisfaction, health_satisfaction,
    tenure, net_income, work_time_weekly, total_years_unemployment, 
    worr_job_dummy, worr_financial_dummy, worr_economic_dummy,
    male, age, university_dummy, married_dummy, white_collar_dummy, self_employed_dummy
  ) %>%
  na.omit()  # Remove missing values

# Check class distribution in y
class_distribution <- table(lasso_data$health_decline_2yrs)
print(class_distribution)

## 
##     0     1 
## 55840 18486

# Split the data into training and test data
set.seed(12345) # For reproducibility
trainIndex <- createDataPartition (lasso_data$health_in_2yrs, p = 0.7, list = FALSE)
# Convert trainIndex to a vector
trainIndex <- as.vector(trainIndex)
# Use the vector to split the data
trainData <- lasso_data[trainIndex, ]
testData <- lasso_data[-trainIndex, ]
dim(trainData)

## [1] 52030    23

#Standardize variables 
# Define relevant numerical variables as a character vector
numerical_vars <- c(
  "BMI", "smoking_dummy", "life_satisfaction", "health_satisfaction",
  "tenure", "net_income", "work_time_weekly", "total_years_unemployment",
  "worr_job_dummy", "worr_financial_dummy", "worr_economic_dummy",
  "male", "age", "worr_health_dummy", "health", "married_dummy","university_dummy","self_employed_dummy","white_collar_dummy"
)

# Apply pre-processing (center and scale) only to the selected numerical columns
preProcValues <- preProcess(trainData[, numerical_vars], method = c("center", "scale"))

# Standardize the training data 
trainData[, numerical_vars] <- predict(preProcValues, trainData[, numerical_vars])

# Standardize the test data
testData[, numerical_vars] <- predict(preProcValues, testData[, numerical_vars])

# Calculate the number of points in train and test subsets
train_size <- nrow(trainData)
test_size <- nrow(testData)

# Create a data frame with the counts for waffle plot
data_proportion <- c(`Train Data` = train_size, `Test Data` = test_size)

# Create the waffle plot
waffle(data_proportion / sum(data_proportion) * 100, 
       rows = 10, # Adjusted number of rows for granularity
       title = "Proportion of Data Points in Training and Test Sets",
       colors = c("#1E2B4F", "#F00000"))

set.seed(12345)

# Set up the training control
# Exclude pid and syear and the outcome variable to avoid overfitting
trainData <- trainData %>% select(-pid, -syear, -health_decline_2yrs)
testData <- testData %>% select(-pid, -syear, -health_decline_2yrs)

# Define cross-validation as the method and 10 folds 
train_control <- trainControl(method = "cv", number = 10)

# Train the LASSO model
lasso_model <- train(
  # use 'health_decline_2yrs' as the dependent and all others as independent variables
  health_in_2yrs ~ ., 
  # specify the traininf data
  data = trainData,
  # We want to use the LASSO method (glmnet)
  method = "glmnet",
  # Use the predefined training specification
  trControl = train_control,
  # Define what values for lambda we should try (tuning)
  tuneGrid = expand.grid(alpha = 1, lambda = seq(0.001, 0.5, by = 0.001))  
)

## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.

# Display the best lambda value and model summary
print(lasso_model$bestTune)

##   alpha lambda
## 1     1  0.001

# Visualize the cross-validation results
ggplot(lasso_model) +
  labs(
    title = "LASSO Model Cross-Validation Results",
    subtitle = "RMSE vs. Log(Lambda) Across Cross-Validation Folds",
    x = "Log(Lambda)",  # X-axis represents lambda values (log-scaled)
    y = "RMSE"          # Y-axis represents cross-validated RMSE
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis labels
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis labels
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),
    plot.subtitle = element_text(size = 12, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 20, b = 20, l = 20)  # Add spacing around the plot
  )

#Save Graph
ggsave("lasso_plot.png", plot = last_plot(), width = 16, height = 8, dpi = 300)
# Model Evaluation
# Predict on the test set
predictions <- predict(lasso_model, newdata = testData)

# Calculate RMSE and R-squared
rmse <- RMSE(predictions, testData$health_in_2yrs)
r2 <- R2(predictions, testData$health_in_2yrs)

# Print the evaluation metrics
print(paste0("RMSE: ", rmse))

## [1] "RMSE: 0.722268301691922"

print(paste0("R-squared: ", r2))

## [1] "R-squared: 0.345957734270469"

# Extract the non-zero coefficients of the best model
coefficients_regression <- coef(lasso_model$finalModel, s = lasso_model$bestTune$lambda)
non_zero_coefficients_regression <- coefficients_regression[coefficients_regression != 0]
print(non_zero_coefficients_regression)

##  [1]  2.648317e+00 -6.027666e-02  2.669041e-01 -6.031442e-02 -2.899668e-02
##  [6]  4.318251e-02  7.531724e-02  1.130334e-03  1.691095e-05 -9.637604e-03
## [11]  3.295679e-03 -1.379412e-02 -3.670387e-03  1.052526e-02 -7.418494e-02
## [16]  3.324199e-02  9.906188e-04  1.159538e-02  1.315751e-03

#Plotting coefficients
# Convert sparse matrix to data frame and filter non-zero coefficients
non_zero_coefficients <- data.frame(
  Variable = rownames(as.matrix(coefficients_regression)),
  Coefficient = as.numeric(as.matrix(coefficients_regression))
) %>%
  filter(Coefficient != 0)  # Keep only non-zero coefficients

# Remove the intercept and rename variables
non_zero_coefficients <- non_zero_coefficients %>%
  filter(Variable != "(Intercept)") %>%  # Remove the intercept
  mutate(
    Variable = case_when(  
      Variable == "health" ~ "Health",
      Variable == "health_satisfaction" ~ "Health Satisfaction",
      Variable == "life_satisfaction" ~ "Life Satisfaction",
      Variable == "educ" ~ "Education",
      Variable == "male" ~ "Gender (Male)",
      Variable == "worr_job_dummy" ~ "Job Worries",
      Variable == "tenure" ~ "Tenure",
      Variable == "work_time_weekly" ~ "Weekly Work Hours",
      Variable == "net_income" ~ "Net Income",
      Variable == "total_years_unemployment" ~ "Total Years Unemployed",
      Variable == "worr_financial_dummy" ~ "Financial Worries",
      Variable == "smoking_dummy" ~ "Smoking",
      Variable == "worr_health_dummy" ~ "Health Worries",
      Variable == "BMI" ~ "BMI",
      Variable == "age" ~ "Age",
      Variable == "university_dummy" ~ "University (Dummy)",
      Variable == "married_dummy" ~ "Married (Dummy)",
      Variable == "white_collar_dummy" ~ "White Collar Job (Dummy)",
      Variable == "self_employed_dummy" ~ "Self Employed (Dummy)",
      TRUE ~ Variable 
    )
  )

# Plotting non-zero coefficients with cleaner labels
ggplot(non_zero_coefficients, aes(x = reorder(Variable, Coefficient), y = Coefficient, fill = Coefficient > 0)) +
  geom_bar(stat = "identity", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Non-Zero Coefficients from Lasso Regression",
    x = "",
    y = "Coefficient Value"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#163E64"),  # Red for negative, dark blue for positive
    guide = "none"  # Remove the legend
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_blank(),  # Remove x-axis title
    axis.title.y = element_blank(),  # Remove y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis text

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space on the right and top/bottom
  )

#Save Graph
ggsave("lasso_coefficients.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

# Visualize the lasso model
plot(lasso_model$finalModel, xvar = "lambda", label = TRUE)

Interpretation

The lasso regression predicting health decline rate shows that current health is an important predictor, followed by health satisfaction, life satisfaction and having a university degree. We also see that longer unemployment, financial worries, smoking, worrying about health, BMI and age have negative coefficients.

Evaluating the distribution of our next outcome variable: Health decline in 2 years -dummy-

# Create the bar plot
ggplot(main, aes(x = factor(health_decline_2yrs))) +
  geom_bar(fill = c("#1E2B4F", "#FF0000"), color = "black") +  # Dark blue for 'No', Red for 'Yes'
  labs(
    title = "Distribution of Health Decline Over 2 Years",
    x = "Health Decline (0 = No, 1 = Yes)",
    y = "Count"
  ) +
  theme_minimal(base_size = 14) +  # Clean aesthetic
  theme(
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, margin = ggplot2::margin(b = 10)),
    axis.title.x = element_text(size = 14, color = "#1E2B4F"),
    axis.title.y = element_text(size = 14, color = "#1E2B4F"),
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_rect(fill = "white", color = NA)
  )

For most participants, health does not decline in 2 years.

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable

# Split the data into training and test data
set.seed(12345) # For reproducibility
trainIndex <- createDataPartition(lasso_data$health_decline_2yrs, p = 0.7, list = FALSE)
# Convert trainIndex to a vector
trainIndex <- as.vector(trainIndex)
# Use the vector to split the data
trainData <- lasso_data[trainIndex, ]
testData <- lasso_data[-trainIndex, ]

# Standardize numerical variables
# Define relevant numerical variables as a character vector
numerical_vars <- c(
  "BMI", "smoking_dummy", "life_satisfaction", "health_satisfaction",
  "tenure", "net_income", "work_time_weekly", "total_years_unemployment",
  "worr_job_dummy", "worr_financial_dummy", "worr_economic_dummy",
  "male", "age",  "worr_health_dummy", "health", "married_dummy","university_dummy","self_employed_dummy","white_collar_dummy"
)

# Apply pre-processing (center and scale) only to the selected numerical columns
preProcValues <- preProcess(trainData[, numerical_vars], method = c("center", "scale"))

# Standardize the training data
trainData[, numerical_vars] <- predict(preProcValues, trainData[, numerical_vars])

# Standardize the test data
testData[, numerical_vars] <- predict(preProcValues, testData[, numerical_vars])

# Exclude pid and syear and the outcome variable to avoid overfitting
trainData <- trainData %>% select(-pid, -syear, -health_in_2yrs)
testData <- testData %>% select(-pid, -syear, health_in_2yrs)

# Convert health_decline_2yrs to a factor
trainData$health_decline_2yrs <- factor(trainData$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))
testData$health_decline_2yrs <- factor(testData$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))

# Set up the training control
train_control <- trainControl(method = "cv", number = 10, classProbs = TRUE, summaryFunction = twoClassSummary)

# Train the LASSO model for classification
set.seed(12345)
lasso_model <- train(
  health_decline_2yrs ~ .,  
  data = trainData,
  method = "glmnet",        # Specify LASSO
  family = "binomial",      # Classification for binary outcome
  trControl = train_control,  # Use predefined training control
  tuneGrid = expand.grid(alpha = 1, lambda = seq(0.001, 0.5, by = 0.001)), # LASSO tuning grid
  metric = "ROC"  # Use ROC as the evaluation metric
)

# Display the best lambda value and model summary
print(lasso_model$bestTune)

##   alpha lambda
## 1     1  0.001

# Visualize the cross-validation results
plot(lasso_model)

# Extract the cross-validation results
cv_results <- lasso_model$results

# Create a ggplot visualization
ggplot(cv_results, aes(x = log(lambda), y = ROC, color = ROC)) +
  geom_point(size = 2, alpha = 0.8) +  # Add points for each lambda value
  geom_line(size = 1) +  # Add a line to connect points
  labs(
    title = "LASSO Model Cross-Validation Results",
    subtitle = "ROC vs. Log(Lambda) Across Cross-Validation Folds",
    x = "Log(Lambda)",
    y = "ROC"
  ) +
  scale_color_gradient(low = "#A6CEE3", high = "#1E2B4F") +  # Gradient from light blue to dark blue
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis text
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Remove legend
    legend.position = "none" 

  )

#Save Graph
ggsave("lasso_model_classification.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

# Model Evaluation
# Predict probabilities on the test set
lasso_predictions <- predict(lasso_model, newdata = testData, type = "prob")

# Predict binary outcomes (threshold = 0.5)
predicted_classes <- ifelse(lasso_predictions[, "Yes"] > 0.5, "Yes", "No")

# Confusion matrix
conf_matrix <- confusionMatrix(factor(predicted_classes, levels = c("No", "Yes")), 
                               factor(testData$health_decline_2yrs, levels = c("No", "Yes")))
print(conf_matrix)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    No   Yes
##        No  16095  4156
##        Yes   751  1295
##                                           
##                Accuracy : 0.7799          
##                  95% CI : (0.7744, 0.7853)
##     No Information Rate : 0.7555          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.2447          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
##                                           
##             Sensitivity : 0.9554          
##             Specificity : 0.2376          
##          Pos Pred Value : 0.7948          
##          Neg Pred Value : 0.6329          
##              Prevalence : 0.7555          
##          Detection Rate : 0.7218          
##    Detection Prevalence : 0.9082          
##       Balanced Accuracy : 0.5965          
##                                           
##        'Positive' Class : No              
##

# Evaluate model performance
print(paste0("Accuracy: ", conf_matrix$overall["Accuracy"]))

## [1] "Accuracy: 0.779925550522492"

print(paste0("Sensitivity: ", conf_matrix$byClass["Sensitivity"]))

## [1] "Sensitivity: 0.955419684198029"

print(paste0("Specificity: ", conf_matrix$byClass["Specificity"]))

## [1] "Specificity: 0.237571087873785"

For health decline in 2 years as outcome, the lasso classification has an accuracy of 77.55% with a sensitivity of 95% and a specificity of 23%. The model is highly sensitive, meaning it rarely misses a true case of health decline (low false negatives). However, its low specificity means it over-predicts health decline, incorrectly flagging many people as at risk when they won’t actually experience decline. This could be problematic, that is why we look at other models like the Random Forest.

# Convert sparse matrix to data frame and filter non-zero coefficients
coefficients <- coef(lasso_model$finalModel, s = lasso_model$bestTune$lambda)

non_zero_coefficients <- data.frame(
  Variable = rownames(as.matrix(coefficients)),
  Coefficient = as.numeric(as.matrix(coefficients))
) %>%
  filter(Coefficient != 0)  # Keep only non-zero coefficients

# Remove the intercept and rename variables
non_zero_coefficients <- non_zero_coefficients %>%
  filter(Variable != "(Intercept)") %>%  # Remove the intercept
  mutate(
    Variable = case_when(  # Rename variables for cleaner labels
      Variable == "health" ~ "Health",
      Variable == "health_satisfaction" ~ "Health Satisfaction",
      Variable == "life_satisfaction" ~ "Life Satisfaction",
      Variable == "educ" ~ "Education Level",
      Variable == "male" ~ "Gender (Male=1)",
      Variable == "worr_job_dummy" ~ "Job Worries (Dummy)",
      Variable == "tenure" ~ "Tenure",
      Variable == "work_time_weekly" ~ "Work Time Weekly",
      Variable == "net_income" ~ "Net Income",
      Variable == "total_years_unemployment" ~ "Total Years Unemployed",
      Variable == "worr_financial_dummy" ~ "Financial Worries (Dummy)",
      Variable == "smoking_dummy" ~ "Smoking (Dummy)",
      Variable == "worr_health_dummy" ~ "Worries About Health (Dummy)",
      Variable == "worr_economic_dummy" ~ "Worries About the Economy (Dummy)",
      Variable == "BMI" ~ "BMI",
      Variable == "age" ~ "Age",
      Variable == "university_dummy" ~ "University (Dummy)",
      Variable == "married_dummy" ~ "Married (Dummy)",
      Variable == "white_collar_dummy" ~ "White Collar Job (Dummy)",
      Variable == "self_employed_dummy" ~ "Self Employed (Dummy)",
      TRUE ~ Variable 
    )
  )

# Plotting non-zero coefficients with cleaner labels
ggplot(non_zero_coefficients, aes(x = reorder(Variable, Coefficient), y = Coefficient, fill = Coefficient > 0)) +
  geom_bar(stat = "identity", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Non-Zero Coefficients from Lasso Classification",
    x = "",
    y = "Coefficient Value"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#1E2B4F"),  # Red for negative, dark blue for positive
    guide = "none"  # Remove the legend
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_blank(),  # Remove x-axis title
    axis.title.y = element_blank(),  # Remove y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis text

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

#Save Graph
ggsave("lasso_coefficients_classification.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

The most important predictor in our model is health, followed by BMI, worries about health, health satisfaction, and having a university degree. Because health impacts our model heavily, we try to exclude it and see if our results vary significantly.

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable, excluding Health in t-1

# Split the data into training and test data
set.seed(12345) # For reproducibility
trainIndex <- createDataPartition(lasso_data$health_decline_2yrs, p = 0.7, list = FALSE)
# Convert trainIndex to a vector
trainIndex <- as.vector(trainIndex)
# Use the vector to split the data
trainData <- lasso_data[trainIndex, ]
testData <- lasso_data[-trainIndex, ]

# Standardize numerical variables
# Define relevant numerical variables as a character vector
numerical_vars <- c(
  "BMI", "smoking_dummy", "life_satisfaction", "health_satisfaction",
  "tenure", "net_income", "work_time_weekly", "total_years_unemployment",
  "worr_job_dummy", "worr_financial_dummy", "worr_economic_dummy",
  "male", "age",  "worr_health_dummy","married_dummy","university_dummy","self_employed_dummy","white_collar_dummy"
)

# Apply pre-processing (center and scale) only to the selected numerical columns
preProcValues <- preProcess(trainData[, numerical_vars], method = c("center", "scale"))

# Standardize the training data
trainData[, numerical_vars] <- predict(preProcValues, trainData[, numerical_vars])

# Standardize the test data
testData[, numerical_vars] <- predict(preProcValues, testData[, numerical_vars])

# Exclude pid and syear and the outcome variable to avoid overfitting and exclude health here too
trainData <- trainData %>% select(-pid, -syear, -health_in_2yrs, -health)
testData <- testData %>% select(-pid, -syear, health_in_2yrs, -health)

# Convert health_decline_2yrs to a factor
trainData$health_decline_2yrs <- factor(trainData$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))
testData$health_decline_2yrs <- factor(testData$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))

# Set up the training control
train_control <- trainControl(method = "cv", number = 10, classProbs = TRUE, summaryFunction = twoClassSummary)

# Train the LASSO model for classification
set.seed(12345)
lasso_model <- train(
  health_decline_2yrs ~ .,  
  data = trainData,
  method = "glmnet",        # Specify LASSO
  family = "binomial",      # Classification for binary outcome
  trControl = train_control,  # Use predefined training control
  tuneGrid = expand.grid(alpha = 1, lambda = seq(0.001, 0.5, by = 0.001)), # LASSO tuning grid
  metric = "ROC"  # Use ROC as the evaluation metric
)

# Display the best lambda value and model summary
print(lasso_model$bestTune)

##   alpha lambda
## 1     1  0.001

# Visualize the cross-validation results
plot(lasso_model)

# Extract the cross-validation results
cv_results <- lasso_model$results

# Create a ggplot visualization
ggplot(cv_results, aes(x = log(lambda), y = ROC, color = ROC)) +
  geom_point(size = 2, alpha = 0.8) +  # Add points for each lambda value
  geom_line(size = 1) +  # Add a line to connect points
  labs(
    title = "LASSO Model Cross-Validation Results",
    subtitle = "ROC vs. Log(Lambda) Across Cross-Validation Folds",
    x = "Log(Lambda)",
    y = "ROC"
  ) +
  scale_color_gradient(low = "#A6CEE3", high = "#1E2B4F") +  # Gradient from light blue to dark blue
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis text
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title and subtitle styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold subtitle
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  # Add more space around the plot
    
    # Remove legend
    legend.position = "none" 

  )

#Save Graph
ggsave("lasso_model_classification_no_health.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

# Model Evaluation
# Predict probabilities on the test set
predictions <- predict(lasso_model, newdata = testData, type = "prob")

# Predict binary outcomes (threshold = 0.5)
predicted_classes <- ifelse(predictions[, "Yes"] > 0.5, "Yes", "No")

# Confusion matrix
conf_matrix <- confusionMatrix(factor(predicted_classes, levels = c("No", "Yes")), 
                               factor(testData$health_decline_2yrs, levels = c("No", "Yes")))
print(conf_matrix)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    No   Yes
##        No  16845  5450
##        Yes     1     1
##                                           
##                Accuracy : 0.7555          
##                  95% CI : (0.7498, 0.7612)
##     No Information Rate : 0.7555          
##     P-Value [Acc > NIR] : 0.5036          
##                                           
##                   Kappa : 2e-04           
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.9999406       
##             Specificity : 0.0001835       
##          Pos Pred Value : 0.7555506       
##          Neg Pred Value : 0.5000000       
##              Prevalence : 0.7555276       
##          Detection Rate : 0.7554828       
##    Detection Prevalence : 0.9999103       
##       Balanced Accuracy : 0.5000620       
##                                           
##        'Positive' Class : No              
##

# Evaluate model performance
print(paste0("Accuracy: ", conf_matrix$overall["Accuracy"]))

## [1] "Accuracy: 0.755527649459569"

print(paste0("Sensitivity: ", conf_matrix$byClass["Sensitivity"]))

## [1] "Sensitivity: 0.999940638727294"

print(paste0("Specificity: ", conf_matrix$byClass["Specificity"]))

## [1] "Specificity: 0.000183452577508714"

Excluding health, the specificity is even lower, with the Lasso model only predicting the right class. We get an accuracy of 75%, a sensitivity of 99.99% and a specificity of 0.01%. The model is unusable in its current form because it flags nearly everyone as experiencing health decline, making it unreliable for targeted interventions.

# Convert sparse matrix to data frame and filter non-zero coefficients
coefficients <- coef(lasso_model$finalModel, s = lasso_model$bestTune$lambda)

non_zero_coefficients <- data.frame(
  Variable = rownames(as.matrix(coefficients)),
  Coefficient = as.numeric(as.matrix(coefficients))
) %>%
  filter(Coefficient != 0)  # Keep only non-zero coefficients

# Remove the intercept and rename variables
non_zero_coefficients <- non_zero_coefficients %>%
  filter(Variable != "(Intercept)") %>%  # Remove the intercept
  mutate(
    Variable = case_when(  # Rename variables for cleaner labels
      Variable == "health_satisfaction" ~ "Health Satisfaction",
      Variable == "life_satisfaction" ~ "Life Satisfaction",
      Variable == "educ" ~ "Education Level",
      Variable == "male" ~ "Gender (Male=1)",
      Variable == "worr_job_dummy" ~ "Job Worries (Dummy)",
      Variable == "tenure" ~ "Tenure",
      Variable == "work_time_weekly" ~ "Work Time Weekly",
      Variable == "net_income" ~ "Net Income",
      Variable == "total_years_unemployment" ~ "Total Years Unemployed",
      Variable == "worr_financial_dummy" ~ "Financial Worries (Dummy)",
      Variable == "smoking_dummy" ~ "Smoking (Dummy)",
      Variable == "worr_health_dummy" ~ "Worries About Health (Dummy)",
      Variable == "worr_economic_dummy" ~ "Worries About the Economy (Dummy)",
      Variable == "BMI" ~ "BMI",
      Variable == "age" ~ "Age",
      Variable == "university_dummy" ~ "University (Dummy)",
      Variable == "married_dummy" ~ "Married (Dummy)",
      Variable == "white_collar_dummy" ~ "White Collar Job (Dummy)",
      Variable == "self_employed_dummy" ~ "Self Employed (Dummy)",
      TRUE ~ Variable 
    )
  )

# Plotting non-zero coefficients with cleaner labels
ggplot(non_zero_coefficients, aes(x = reorder(Variable, Coefficient), y = Coefficient, fill = Coefficient > 0)) +
  geom_bar(stat = "identity", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Non-Zero Coefficients from Lasso Classification",
    x = "",
    y = "Coefficient Value"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#1E2B4F"),  # Red for negative, dark blue for positive
    guide = "none"  # Remove the legend
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_blank(),  # Remove x-axis title
    axis.title.y = element_blank(),  # Remove y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis text

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

#Save Graph
ggsave("lasso_coefficients_classification_no_health.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

Health satisfaction then becomes the most important predictor. Followed by BMI, Smoking, not having a University degree, being a female, not being married, and worrying about health. These results align with expectations, but the predictors identified are similar to the one including the Health predictor, and the specificity being close to 0, therefore in the RF, we will still include health.

Random Forest Classification: Health decline in 2 years -dummy- as an outcome Variable

set.seed(12345)
# Convert data to panel format
panel_data <- pdata.frame(main, index = c("pid", "syear"))  # pid = individual ID, syear = time

# Define relevant numerical variables as a character vector
numerical_vars <- c(
  "BMI", "smoking_dummy", "life_satisfaction", "health_satisfaction",
  "tenure", "net_income", "work_time_weekly", "total_years_unemployment",
  "worr_job_dummy", "worr_financial_dummy", "worr_economic_dummy",
  "male", "age",  "worr_health_dummy", "health", "married_dummy","university_dummy","self_employed_dummy","white_collar_dummy"
)

# Create rf_data by removing specific columns
rf_data <- panel_data %>%
  dplyr::select(
     health_decline_2yrs, worr_health_dummy, health, BMI, smoking_dummy, life_satisfaction, health_satisfaction,
    tenure, net_income, work_time_weekly, total_years_unemployment, 
    worr_job_dummy, worr_financial_dummy, worr_economic_dummy,
    male, age, university_dummy, married_dummy, white_collar_dummy, self_employed_dummy
  ) %>%
  na.omit()  # Remove missing values


# Ensure health_decline_2yrs Is a Factor
rf_data$health_decline_2yrs <- factor(rf_data$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))

# Dynamically create the formula
class_tree_formula <- as.formula(paste("health_decline_2yrs ~", paste(numerical_vars, collapse = " + ")))

# Fit the decision tree
class_tree <- rpart(
  formula = class_tree_formula,
  data = rf_data,
  method = "class",
  control = rpart.control(
    cp = 0.001,       # Lower complexity parameter to allow more splits
    minsplit = 10,    # Minimum number of observations required to split
    minbucket = 5,    # Minimum observations in a terminal node
    maxdepth = 10     # Maximum depth of the tree
  )
)

# Plot the decision tree
rpart.plot(class_tree, main = "Decision Tree: Classification")

# Plot the decision tree with explicit splits
rpart.plot(class_tree, main = "Decision Tree: Classification", type = 5)

# Building the classification model

# Create a training and test dataset
trainIndex <- createDataPartition (rf_data$health_decline_2yrs, p = 0.7, list = FALSE)
# Convert trainIndex to a vector
trainIndex <- as.vector(trainIndex)
trainData <- rf_data[trainIndex, ]
testData <- rf_data[-trainIndex, ]
dim(trainData)

## [1] 52029    20

dim(testData)

## [1] 22297    20

# Creates a data frame (tuning_grid) where trees ranges from 5 to 400 in 
# steps of 5. The rmse column is initialized with NA to be filled later.
tuning_grid <- expand.grid(
  trees = seq(5, 400, by = 5),
  rmse  = NA
)


for(i in seq_len(nrow(tuning_grid))) { # Iterates over each row of the tuning_grid.
  
  # Fits a random forest model 
  fit <- ranger(
  formula    = class_tree_formula, 
  data       = trainData, 
  num.trees  = tuning_grid$trees[i],
  mtry       = sqrt(5), 
  verbose    = FALSE,
  seed       = 123
  )
  # Stores the RMSE of the model 
  tuning_grid$rmse[i] <- sqrt(fit$prediction.error)
}

We see in the tree again that health is the stronger predictor, followed by health satisfaction, having a university degree, worrying about health and lfie satisfaction. These predictors align with the results found using the Lasso model.

# Plot the rmse against then number of trees
ggplot(tuning_grid, aes(trees, rmse)) + 
  geom_line()

# Plot the RMSE against the number of trees with enhanced theme
ggplot(tuning_grid, aes(x = trees, y = rmse)) + 
  geom_line(color = "#163E64", size = 1) +  # Dark blue line
  geom_point(color = "#1E2B4F", size = 2, alpha = 0.8) +  # Points for emphasis
  labs(
    title = "Random Forest Model Tuning: RMSE vs. Number of Trees",
    x = "Number of Trees",
    y = "RMSE"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  # Dark blue y-axis text
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue x-axis title
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis title

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

#Save Graph
ggsave("rf_rmse.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

We see that the performance of the RMSE asnd therefore the model stabilized at 100 trees and we will be therefore using that number in our model.

# Defines the training scheme to be 5-fold cross-validation
train_control <- trainControl(method = "cv", number = 10)

tune_grid <- expand.grid(
  mtry = seq(3,7,0.05),  # Number of variables randomly sampled at each split
  splitrule = "gini", # Number of trees in the forest
  min.node.size = c(1, 2, 5) # Minimum size of terminal nodes
)

# Train the Random Forest model using ranger in caret
set.seed(12345) # Set seed for reproducibility 
rf_model <- train(
  class_tree_formula, 
  data = trainData, 
  method = "ranger",             
  trControl = train_control, 
  tuneGrid = tune_grid, 
  num.trees = 100 # that we got previously               
)

# Print the best model and results
print(rf_model)

## Random Forest 
## 
## 52029 samples
##    19 predictor
##     2 classes: 'No', 'Yes' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 46826, 46826, 46826, 46826, 46826, 46826, ... 
## Resampling results across tuning parameters:
## 
##   mtry  min.node.size  Accuracy   Kappa    
##   3.00  1              0.7747409  0.2340849
##   3.00  2              0.7760863  0.2370829
##   3.00  5              0.7762401  0.2390655
##   3.05  1              0.7756058  0.2371106
##   3.05  2              0.7757981  0.2358881
##   3.05  5              0.7771435  0.2398106
##   3.10  1              0.7763746  0.2378630
##   3.10  2              0.7767975  0.2395536
##   3.10  5              0.7758364  0.2351748
##   3.15  1              0.7761440  0.2374573
##   3.15  2              0.7758941  0.2364420
##   3.15  5              0.7767590  0.2375411
##   3.20  1              0.7765669  0.2389878
##   3.20  2              0.7760095  0.2356203
##   3.20  5              0.7757788  0.2356257
##   3.25  1              0.7755097  0.2351081
##   3.25  2              0.7760479  0.2367388
##   3.25  5              0.7755097  0.2348899
##   3.30  1              0.7757788  0.2354075
##   3.30  2              0.7767398  0.2405017
##   3.30  5              0.7754713  0.2356876
##   3.35  1              0.7760670  0.2382710
##   3.35  2              0.7767013  0.2399008
##   3.35  5              0.7762017  0.2373783
##   3.40  1              0.7764707  0.2387085
##   3.40  2              0.7759134  0.2360951
##   3.40  5              0.7766245  0.2397463
##   3.45  1              0.7756443  0.2366681
##   3.45  2              0.7762978  0.2378150
##   3.45  5              0.7765668  0.2399170
##   3.50  1              0.7754136  0.2353500
##   3.50  2              0.7752406  0.2346002
##   3.50  5              0.7764131  0.2389285
##   3.55  1              0.7747601  0.2325160
##   3.55  2              0.7776239  0.2429595
##   3.55  5              0.7757981  0.2372910
##   3.60  1              0.7755674  0.2361288
##   3.60  2              0.7757404  0.2352145
##   3.60  5              0.7769127  0.2387285
##   3.65  1              0.7754136  0.2362034
##   3.65  2              0.7755290  0.2357594
##   3.65  5              0.7760095  0.2367791
##   3.70  1              0.7767206  0.2394676
##   3.70  2              0.7750677  0.2328169
##   3.70  5              0.7762593  0.2376845
##   3.75  1              0.7754328  0.2348686
##   3.75  2              0.7759133  0.2355549
##   3.75  5              0.7755674  0.2342761
##   3.80  1              0.7764323  0.2387786
##   3.80  2              0.7759134  0.2393317
##   3.80  5              0.7753752  0.2339301
##   3.85  1              0.7757981  0.2371430
##   3.85  2              0.7758172  0.2357210
##   3.85  5              0.7777008  0.2426346
##   3.90  1              0.7763938  0.2392017
##   3.90  2              0.7764707  0.2397297
##   3.90  5              0.7764131  0.2390182
##   3.95  1              0.7757788  0.2355941
##   3.95  2              0.7752022  0.2334880
##   3.95  5              0.7755673  0.2346318
##   4.00  1              0.7747410  0.2492850
##   4.00  2              0.7757788  0.2519603
##   4.00  5              0.7759517  0.2518777
##   4.05  1              0.7761632  0.2537870
##   4.05  2              0.7754713  0.2516936
##   4.05  5              0.7766821  0.2538815
##   4.10  1              0.7753944  0.2515740
##   4.10  2              0.7758557  0.2515784
##   4.10  5              0.7754905  0.2503870
##   4.15  1              0.7756443  0.2506440
##   4.15  2              0.7757403  0.2537247
##   4.15  5              0.7762401  0.2541528
##   4.20  1              0.7755481  0.2522313
##   4.20  2              0.7753560  0.2514512
##   4.20  5              0.7765667  0.2550969
##   4.25  1              0.7757403  0.2538269
##   4.25  2              0.7767590  0.2556336
##   4.25  5              0.7757019  0.2507936
##   4.30  1              0.7754520  0.2530853
##   4.30  2              0.7754136  0.2511930
##   4.30  5              0.7755866  0.2516565
##   4.35  1              0.7755289  0.2521661
##   4.35  2              0.7751253  0.2499829
##   4.35  5              0.7756058  0.2521432
##   4.40  1              0.7758557  0.2533691
##   4.40  2              0.7760478  0.2542294
##   4.40  5              0.7760671  0.2537463
##   4.45  1              0.7750869  0.2516057
##   4.45  2              0.7742028  0.2462294
##   4.45  5              0.7764515  0.2532783
##   4.50  1              0.7756827  0.2532859
##   4.50  2              0.7757019  0.2508686
##   4.50  5              0.7757788  0.2524444
##   4.55  1              0.7741451  0.2473647
##   4.55  2              0.7747217  0.2489687
##   4.55  5              0.7756443  0.2530595
##   4.60  1              0.7754905  0.2518587
##   4.60  2              0.7758749  0.2524220
##   4.60  5              0.7756635  0.2518185
##   4.65  1              0.7766820  0.2548883
##   4.65  2              0.7751061  0.2504934
##   4.65  5              0.7753175  0.2495882
##   4.70  1              0.7750292  0.2507744
##   4.70  2              0.7758557  0.2537782
##   4.70  5              0.7759902  0.2524600
##   4.75  1              0.7763170  0.2557246
##   4.75  2              0.7756827  0.2503268
##   4.75  5              0.7760479  0.2530078
##   4.80  1              0.7757019  0.2534186
##   4.80  2              0.7753944  0.2516710
##   4.80  5              0.7757980  0.2511784
##   4.85  1              0.7752406  0.2514665
##   4.85  2              0.7756443  0.2523174
##   4.85  5              0.7758364  0.2523747
##   4.90  1              0.7747217  0.2498598
##   4.90  2              0.7760094  0.2540426
##   4.90  5              0.7757020  0.2523181
##   4.95  1              0.7746833  0.2485795
##   4.95  2              0.7751638  0.2508531
##   4.95  5              0.7758365  0.2529668
##   5.00  1              0.7739914  0.2548015
##   5.00  2              0.7751638  0.2586580
##   5.00  5              0.7757404  0.2579347
##   5.05  1              0.7739913  0.2549194
##   5.05  2              0.7752983  0.2580353
##   5.05  5              0.7753175  0.2578476
##   5.10  1              0.7749139  0.2575995
##   5.10  2              0.7748178  0.2568274
##   5.10  5              0.7746256  0.2549069
##   5.15  1              0.7756058  0.2598365
##   5.15  2              0.7750100  0.2580501
##   5.15  5              0.7756635  0.2577634
##   5.20  1              0.7744718  0.2571554
##   5.20  2              0.7743565  0.2559029
##   5.20  5              0.7753944  0.2578224
##   5.25  1              0.7752407  0.2597149
##   5.25  2              0.7738952  0.2540663
##   5.25  5              0.7749332  0.2566353
##   5.30  1              0.7753175  0.2596653
##   5.30  2              0.7750293  0.2575151
##   5.30  5              0.7737607  0.2534463
##   5.35  1              0.7749716  0.2584421
##   5.35  2              0.7738760  0.2546184
##   5.35  5              0.7749139  0.2588180
##   5.40  1              0.7750869  0.2588088
##   5.40  2              0.7743565  0.2560544
##   5.40  5              0.7765283  0.2606028
##   5.45  1              0.7755482  0.2599662
##   5.45  2              0.7742796  0.2557642
##   5.45  5              0.7755674  0.2577775
##   5.50  1              0.7747409  0.2573078
##   5.50  2              0.7747409  0.2569846
##   5.50  5              0.7756636  0.2607584
##   5.55  1              0.7741259  0.2559358
##   5.55  2              0.7742604  0.2558438
##   5.55  5              0.7757403  0.2594234
##   5.60  1              0.7756827  0.2599172
##   5.60  2              0.7758749  0.2609193
##   5.60  5              0.7752406  0.2568751
##   5.65  1              0.7744910  0.2554753
##   5.65  2              0.7745872  0.2573445
##   5.65  5              0.7751061  0.2565600
##   5.70  1              0.7743373  0.2563305
##   5.70  2              0.7753943  0.2596180
##   5.70  5              0.7745679  0.2566162
##   5.75  1              0.7744142  0.2562216
##   5.75  2              0.7735685  0.2534241
##   5.75  5              0.7747602  0.2573342
##   5.80  1              0.7742796  0.2557234
##   5.80  2              0.7742988  0.2556802
##   5.80  5              0.7751061  0.2571349
##   5.85  1              0.7760478  0.2624471
##   5.85  2              0.7743950  0.2567454
##   5.85  5              0.7751061  0.2576581
##   5.90  1              0.7747793  0.2566316
##   5.90  2              0.7744911  0.2562838
##   5.90  5              0.7745871  0.2549600
##   5.95  1              0.7748563  0.2580809
##   5.95  2              0.7746641  0.2576160
##   5.95  5              0.7740106  0.2526772
##   6.00  1              0.7736838  0.2589325
##   6.00  2              0.7740489  0.2581055
##   6.00  5              0.7740874  0.2582697
##   6.05  1              0.7747602  0.2636607
##   6.05  2              0.7738376  0.2588621
##   6.05  5              0.7735685  0.2560169
##   6.10  1              0.7743373  0.2612351
##   6.10  2              0.7739144  0.2582348
##   6.10  5              0.7739913  0.2584495
##   6.15  1              0.7742412  0.2612158
##   6.15  2              0.7744718  0.2598642
##   6.15  5              0.7742796  0.2594168
##   6.20  1              0.7751829  0.2639506
##   6.20  2              0.7737030  0.2583367
##   6.20  5              0.7738376  0.2583441
##   6.25  1              0.7754906  0.2639597
##   6.25  2              0.7741451  0.2584713
##   6.25  5              0.7729535  0.2541626
##   6.30  1              0.7738376  0.2589949
##   6.30  2              0.7747985  0.2628174
##   6.30  5              0.7744911  0.2587514
##   6.35  1              0.7744910  0.2618390
##   6.35  2              0.7749909  0.2634042
##   6.35  5              0.7741259  0.2579373
##   6.40  1              0.7731456  0.2569705
##   6.40  2              0.7749716  0.2638864
##   6.40  5              0.7745680  0.2598181
##   6.45  1              0.7747410  0.2622312
##   6.45  2              0.7742219  0.2601779
##   6.45  5              0.7751446  0.2610109
##   6.50  1              0.7737799  0.2599907
##   6.50  2              0.7748563  0.2616665
##   6.50  5              0.7741643  0.2578784
##   6.55  1              0.7740682  0.2599061
##   6.55  2              0.7747217  0.2625540
##   6.55  5              0.7736454  0.2560463
##   6.60  1              0.7743758  0.2614112
##   6.60  2              0.7741259  0.2589505
##   6.60  5              0.7752022  0.2624524
##   6.65  1              0.7736838  0.2588843
##   6.65  2              0.7744719  0.2615920
##   6.65  5              0.7738183  0.2572813
##   6.70  1              0.7739913  0.2616465
##   6.70  2              0.7725114  0.2536039
##   6.70  5              0.7747794  0.2605539
##   6.75  1              0.7738376  0.2605314
##   6.75  2              0.7739721  0.2594515
##   6.75  5              0.7755097  0.2633352
##   6.80  1              0.7734724  0.2576752
##   6.80  2              0.7734725  0.2584535
##   6.80  5              0.7741259  0.2600103
##   6.85  1              0.7737414  0.2595692
##   6.85  2              0.7744142  0.2607416
##   6.85  5              0.7738184  0.2564479
##   6.90  1              0.7736646  0.2587536
##   6.90  2              0.7740106  0.2593117
##   6.90  5              0.7750484  0.2618440
##   6.95  1              0.7721654  0.2534881
##   6.95  2              0.7731841  0.2569284
##   6.95  5              0.7739529  0.2578001
##   7.00  1              0.7730687  0.2599852
##   7.00  2              0.7736262  0.2617328
##   7.00  5              0.7743565  0.2614719
## 
## Tuning parameter 'splitrule' was held constant at a value of gini
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were mtry = 3.85, splitrule = gini
##  and min.node.size = 5.

# Make predictions on the test set
rf_predictions <- predict(rf_model, newdata = testData)

The values of mtry or the number of predictors randomly selected at each split in the decision trees and minimum node size are 3.85 and 5 respectively to give an accuracy of 77.7% and Kappa value of 0.2426346. Kappa measures agreement beyond chance (range: 0 to 1). 0.24 Kappa suggests low to moderate agreement, meaning the model is only slightly better than chance in handling class imbalance.

# Confusion matrix to evaluate performance
rf_predictions <- factor(rf_predictions, levels = c("No", "Yes"))
confusionMatrix(rf_predictions, testData$health_decline_2yrs, positive = "Yes")

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    No   Yes
##        No  16042  4209
##        Yes   710  1336
##                                           
##                Accuracy : 0.7794          
##                  95% CI : (0.7739, 0.7848)
##     No Information Rate : 0.7513          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.2517          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
##                                           
##             Sensitivity : 0.24094         
##             Specificity : 0.95762         
##          Pos Pred Value : 0.65298         
##          Neg Pred Value : 0.79216         
##              Prevalence : 0.24869         
##          Detection Rate : 0.05992         
##    Detection Prevalence : 0.09176         
##       Balanced Accuracy : 0.59928         
##                                           
##        'Positive' Class : Yes             
##

# Fit the final model 'rf_model'
rf_final <- ranger(
  formula    = class_tree_formula, 
  data       = trainData, 
  num.trees  = 100,           # Number of trees
  probability = TRUE,         # Predict probabilities
  importance = "impurity",    # Variable importance measure
  mtry       = 3.85,          # Number of variables randomly sampled at each split that we got in previous step
  min.node.size = 5,         # Minimum node size that we got in previous step
  seed       = 123            # For reproducibility
)

# Get feature importance
v1 <- vip(rf_final) # Calculate and plot the variable importance
v1$data # Print the variable importance values

# Plot of feature importance
v1_table <- v1$data

# Clean and rename variables
v1_table <- v1_table %>%
  filter(Variable != "(Intercept)") %>%  # Remove the intercept
  mutate(
    Variable = case_when(  # Rename variables for cleaner labels
      Variable == "health" ~ "Health",
      Variable == "health_lag1" ~ "Health of previous year",
      Variable == "health_satisfaction" ~ "Health Satisfaction",
      Variable == "life_satisfaction" ~ "Life Satisfaction",
      Variable == "educ" ~ "Education Level",
      Variable == "male" ~ "Male (Dummy)",
      Variable == "worr_job_dummy" ~ "Job Worries (Dummy)",
      Variable == "tenure" ~ "Tenure",
      Variable == "tenure_lag1" ~ "Tenure of previous year",
      Variable == "work_time_weekly" ~ "Weekly Work Hours",
      Variable == "work_time_weekly_lag1" ~ "Weekly Work Hours of previous year",
      Variable == "net_income" ~ "Net Income",
      Variable == "net_income_lag1" ~ "Net Income of previous year",
      Variable == "total_years_unemployment" ~ "Total Years Unemployed",
      Variable == "worr_financial_dummy" ~ "Financial Worries (Dummy)",
      Variable == "smoking_dummy" ~ "Smoking",
      Variable == "worr_health_dummy" ~ "Health Worries (Dummy)",
      Variable == "BMI" ~ "BMI",
      Variable == "age" ~ "Age",
      Variable == "university_dummy" ~ "University (Dummy)",
      Variable == "married_dummy" ~ "Married (Dummy)",
      Variable == "white_collar_dummy" ~ "White Collar Job (Dummy)",
      Variable == "self_employed_dummy" ~ "Self Employed (Dummy)",
      TRUE ~ Variable 
    )
  )

# Create the bar plot
ggplot(v1_table, aes(x = reorder(Variable, Importance), y = Importance)) +
  geom_bar(stat = "identity", position = "dodge", fill = "#1E2B4F", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Variable Importance from Random Forest",
    x = "",
    y = "Importance"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    panel.background = element_rect(fill = "white", color = NA), # Dark blue background
    plot.background = element_rect(fill = "white", color = NA), # Dark blue outer background
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(), 
    axis.text.x = element_text(size = 12, color = "#1E2B4F"), 
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"), 
    plot.title = element_text(face = "bold", size = 16, hjust = 0.25, color = "#1E2B4F"), # Shift title left and color 
    plot.caption = element_text(color = "#1E2B4F"), 
    axis.title = element_text(color = "#1E2B4F"), 
    legend.position = "none"  # Remove the legend
  )

#Save Graph
ggsave("rf_importance.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

Interpretation

Both Lasso Regression and Random Forest largely highlight similar patterns: • Health seems to be path-related as current health is the strongest predictor for future health decline, • Personal characteristics such as older age or higher BMI as associated with higher probabilities of health decline while being married is associated with a lower probability, • Labor market characteristics like net income and tenure also seem to predict health decline – however, the direction of the effect is not clear. Both models show similar Accuracy above 70%, which reflects the overall model performance quality. Lasso Regression demonstrates high Sensitivity, which means that the model rarely misses health decline cases. On the contrary, Random Forest has a very high Specificity, implying very well identification of “no health decline” cases.

Partial Dependence

# Calculate the Partial Dependence for male
pdp_male <- partial(
  object = rf_final, 
  pred.var = "male", 
  train = trainData,
  prob = TRUE
)

# Calculate the Partial Dependence for bmi
pdp_bmi <- partial(
  object = rf_final, 
  pred.var = "BMI", 
  train = trainData,
  prob = TRUE
)


# Calculate the Partial Dependence for white_collar
pdp_white_collar <- partial(
  object = rf_final, 
  pred.var = "white_collar_dummy", 
  train = trainData,
  prob = TRUE
)
trainData$life_satisfaction <- as.vector(trainData$life_satisfaction)
# Calculate the Partial Dependence for Life Satisfaction
pdp_life <- partial(
  object = rf_final, 
  pred.var = "life_satisfaction", 
  train = trainData,
  prob = TRUE
)

# Calculate the Partial Dependence for age
pdp_age <- partial(
  object = rf_final, 
  pred.var = "age", 
  train = trainData,
  prob = TRUE
)

# Plot the PDP for bmi
p3 <- autoplot(pdp_bmi) +
  ylab("Health Decline Prob")+
  xlab("BMI")+
  theme_minimal()

# Plot the PDP for life_satisfaction
p5 <- autoplot(pdp_life) +
  ylab("Health Decline Prob")+
  xlab("Life Satisfaction")+
  theme_minimal()

# Plot the PDP for age
p6 <- autoplot(pdp_age) +
  ylab("Health Decline Prob")+
  xlab("Age")+
  theme_minimal()

# Combine the plots
(p3 ) /
(p5 ) /
(p6 )

Next steps

Because neither models provided convincing results, we will be performing random undersampling in Lasso and balancing the majority and minority classes.

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable, WITH undersampling

# Convert data to panel format
panel_data <- pdata.frame(main, index = c("pid", "syear"))  # pid = individual ID, syear = time

# Prepare data for LASSO regression
lasso_data <- panel_data %>%
  dplyr::select(
    pid, syear, health_decline_2yrs, health_in_2yrs, worr_health_dummy, health, BMI, smoking_dummy, life_satisfaction, health_satisfaction,
    tenure, net_income, work_time_weekly, total_years_unemployment, 
    worr_job_dummy, worr_financial_dummy, worr_economic_dummy,
    male, age, university_dummy, married_dummy, white_collar_dummy, self_employed_dummy
  ) %>%
  na.omit()  # Remove missing values

# Split the data into training and test data
set.seed(12345) # For reproducibility
trainIndex <- createDataPartition(lasso_data$health_decline_2yrs, p = 0.7, list = FALSE)

# Convert trainIndex to a vector
trainIndex <- as.vector(trainIndex)

# Use the vector to split the data
trainData <- lasso_data[trainIndex, ]
testData <- lasso_data[-trainIndex, ]

# Exclude pid and syear and the outcome variable to avoid overfitting and exclude health here too
trainData <- trainData %>% select(-pid, -syear, -health_in_2yrs)
testData <- testData %>% select(-pid, -syear, health_in_2yrs)


# Define the number of instances to keep (equal to minority class count)
N_target <- sum(trainData$health_decline_2yrs == 1) * 2  # 1:1 ratio

# Perform random undersampling
balanced_data <- ovun.sample(
  health_decline_2yrs ~ .,  # Target variable
  data = trainData,  
  method = "under",  # Perform undersampling
  N = N_target,  # Keep equal numbers in both classes
  seed = 123
)$data  # Extract the balanced dataset

# Check new class distribution
table(balanced_data$health_decline_2yrs)

## 
##     0     1 
## 13035 13035

## We now have a balanced dataset with 13035 occurences of each group.

# Standardize numerical variables **AFTER RESAMPLING**
numerical_vars <- c(
  "BMI", "smoking_dummy", "life_satisfaction", "health_satisfaction",
  "tenure", "net_income", "work_time_weekly", "total_years_unemployment",
  "worr_job_dummy", "worr_financial_dummy", "worr_economic_dummy",
  "male", "age",  "worr_health_dummy", "health", 
  "married_dummy", "university_dummy", "self_employed_dummy", "white_collar_dummy"
)

# Apply pre-processing (center and scale) only to the selected numerical columns
preProcValues <- preProcess(balanced_data[, numerical_vars], method = c("center", "scale"))

# Standardize the training data
balanced_data[, numerical_vars] <- predict(preProcValues, balanced_data[, numerical_vars])

# Standardize the test data
testData[, numerical_vars] <- predict(preProcValues, testData[, numerical_vars])

# Convert `health_decline_2yrs` to factor
balanced_data$health_decline_2yrs <- factor(balanced_data$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))
testData$health_decline_2yrs <- factor(testData$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))


# Set up the training control
train_control <- trainControl(method = "cv", number = 10, classProbs = TRUE, summaryFunction = twoClassSummary)

# Train the LASSO model for classification using the balanced dataset
set.seed(12345)
lasso_model_balanced <- train(
  health_decline_2yrs ~ .,  
  data = balanced_data,
  method = "glmnet",        # Specify LASSO
  family = "binomial",      # Classification for binary outcome
  trControl = train_control,  # Use predefined training control
  tuneGrid = expand.grid(alpha = 1, lambda = seq(0.001, 0.5, by = 0.001)), # LASSO tuning grid
  metric = "ROC"  # Use ROC as the evaluation metric
)

# Display the best lambda value and model summary
print(lasso_model_balanced$bestTune)

##   alpha lambda
## 1     1  0.001

# Extract the cross-validation results
cv_results <- lasso_model_balanced$results

# Create a ggplot visualization for Cross-validation
ggplot(cv_results, aes(x = log(lambda), y = ROC, color = ROC)) +
  geom_point(size = 2, alpha = 0.8) +  # Add points for each lambda value
  geom_line(size = 1) +  # Add a line to connect points
  labs(
    title = "LASSO Balanced Model Cross-Validation Results",
    subtitle = "ROC vs. Log(Lambda) Across Cross-Validation Folds",
    x = "Log(Lambda)",
    y = "ROC"
  ) +
  scale_color_gradient(low = "#A6CEE3", high = "#1E2B4F") +  # Gradient from light blue to dark blue
  theme_minimal(base_size = 14) +
  theme(
    panel.background = element_rect(fill = "white", color = NA),  
    plot.background = element_rect(fill = "white", color = NA),  

    panel.grid.major = element_blank(),  
    panel.grid.minor = element_blank(),  

    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  

    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  

    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  
    legend.position = "none" 
  )

# Save Graph
ggsave("lasso_model_classification_balanced.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

# Model Evaluation on Original Test Set
lasso_predictions_balanced <- predict(lasso_model_balanced, newdata = testData, type = "prob")

# Predict binary outcomes (threshold = 0.5)
predicted_classes <- ifelse(lasso_predictions_balanced[, "Yes"] > 0.5, "Yes", "No")

# Confusion matrix
conf_matrix <- confusionMatrix(factor(predicted_classes, levels = c("No", "Yes")), 
                               factor(testData$health_decline_2yrs, levels = c("No", "Yes")))
print(conf_matrix)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    No   Yes
##        No  11232  1758
##        Yes  5614  3693
##                                           
##                Accuracy : 0.6694          
##                  95% CI : (0.6632, 0.6755)
##     No Information Rate : 0.7555          
##     P-Value [Acc > NIR] : 1               
##                                           
##                   Kappa : 0.2778          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.6667          
##             Specificity : 0.6775          
##          Pos Pred Value : 0.8647          
##          Neg Pred Value : 0.3968          
##              Prevalence : 0.7555          
##          Detection Rate : 0.5037          
##    Detection Prevalence : 0.5826          
##       Balanced Accuracy : 0.6721          
##                                           
##        'Positive' Class : No              
##

# Evaluate model performance
print(paste0("Accuracy: ", conf_matrix$overall["Accuracy"]))

## [1] "Accuracy: 0.669372561331121"

print(paste0("Sensitivity: ", conf_matrix$byClass["Sensitivity"]))

## [1] "Sensitivity: 0.666745815030274"

print(paste0("Specificity: ", conf_matrix$byClass["Specificity"]))

## [1] "Specificity: 0.677490368739681"

# Convert sparse matrix to data frame and filter non-zero coefficients
coefficients <- coef(lasso_model_balanced$finalModel, s = lasso_model_balanced$bestTune$lambda)

non_zero_coefficients <- data.frame(
  Variable = rownames(as.matrix(coefficients)),
  Coefficient = as.numeric(as.matrix(coefficients))
) %>%
  filter(Coefficient != 0)  # Keep only non-zero coefficients

# Remove the intercept and rename variables
non_zero_coefficients <- non_zero_coefficients %>%
  filter(Variable != "(Intercept)") %>%  # Remove the intercept
  mutate(
    Variable = case_when(  # Rename variables for cleaner labels
      Variable == "health" ~ "Health",
      Variable == "health_satisfaction" ~ "Health Satisfaction",
      Variable == "life_satisfaction" ~ "Life Satisfaction",
      Variable == "educ" ~ "Education Level",
      Variable == "male" ~ "Gender (Male=1)",
      Variable == "worr_job_dummy" ~ "Job Worries (Dummy)",
      Variable == "tenure" ~ "Tenure",
      Variable == "work_time_weekly" ~ "Work Time Weekly",
      Variable == "net_income" ~ "Net Income",
      Variable == "total_years_unemployment" ~ "Total Years Unemployed",
      Variable == "worr_financial_dummy" ~ "Financial Worries (Dummy)",
      Variable == "smoking_dummy" ~ "Smoking (Dummy)",
      Variable == "worr_health_dummy" ~ "Worries About Health (Dummy)",
      Variable == "worr_economic_dummy" ~ "Worries About the Economy (Dummy)",
      Variable == "BMI" ~ "BMI",
      Variable == "age" ~ "Age",
      Variable == "university_dummy" ~ "University (Dummy)",
      Variable == "married_dummy" ~ "Married (Dummy)",
      Variable == "white_collar_dummy" ~ "White Collar Job (Dummy)",
      Variable == "self_employed_dummy" ~ "Self Employed (Dummy)",
      TRUE ~ Variable 
    )
  )

# Plotting non-zero coefficients with cleaner labels
ggplot(non_zero_coefficients, aes(x = reorder(Variable, Coefficient), y = Coefficient, fill = Coefficient > 0)) +
  geom_bar(stat = "identity", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Non-Zero Coefficients from Lasso Balanced",
    x = "",
    y = "Coefficient Value"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#1E2B4F"),  # Red for negative, dark blue for positive
    guide = "none"  # Remove the legend
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_blank(),  # Remove x-axis title
    axis.title.y = element_blank(),  # Remove y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis text

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

#Save Graph
ggsave("lasso_coefficients_classification_balanced.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

Again, the important predictors are similar to the ones we have seen in the other models: health, BMI, worrying about one’s health, health satisfaction, not having a university degree, being dissatisfied with life, and being a female. But what is interesting about this undersampled lasso model is that, even though the accuracy is only at 67%, the sensitivity 66.67% and specificity 67.7% are balanced. This suggests that your undersampled LASSO model is handling both classes fairly well.

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable, WITH undersampling, excluding Health in t-1

# Convert data to panel format
panel_data <- pdata.frame(main, index = c("pid", "syear"))  # pid = individual ID, syear = time

# Prepare data for LASSO regression
lasso_data <- panel_data %>%
  dplyr::select(
    pid, syear, health_decline_2yrs, health_in_2yrs, worr_health_dummy, health, BMI, smoking_dummy, life_satisfaction, health_satisfaction,
    tenure, net_income, work_time_weekly, total_years_unemployment, 
    worr_job_dummy, worr_financial_dummy, worr_economic_dummy,
    male, age, university_dummy, married_dummy, white_collar_dummy, self_employed_dummy
  ) %>%
  na.omit()  # Remove missing values

# Split the data into training and test data
set.seed(12345) # For reproducibility
trainIndex <- createDataPartition(lasso_data$health_decline_2yrs, p = 0.7, list = FALSE)

# Convert trainIndex to a vector
trainIndex <- as.vector(trainIndex)

# Use the vector to split the data
trainData <- lasso_data[trainIndex, ]
testData <- lasso_data[-trainIndex, ]

# Exclude pid and syear and the outcome variable to avoid overfitting and exclude health here too
trainData <- trainData %>% select(-pid, -syear, -health_in_2yrs, -health)
testData <- testData %>% select(-pid, -syear, -health_in_2yrs, -health)


# Define the number of instances to keep (equal to minority class count)
N_target <- sum(trainData$health_decline_2yrs == 1) * 2  # 1:1 ratio

# Perform random undersampling
balanced_data <- ovun.sample(
  health_decline_2yrs ~ .,  # Target variable
  data = trainData,  
  method = "under",  # Perform undersampling
  N = N_target,  # Keep equal numbers in both classes
  seed = 123
)$data  # Extract the balanced dataset

# Check new class distribution
table(balanced_data$health_decline_2yrs)

## 
##     0     1 
## 13035 13035

## We now have a balanced dataset with 13035 occurences of each group.

# Standardize numerical variables **AFTER RESAMPLING**
numerical_vars <- c(
  "BMI", "smoking_dummy", "life_satisfaction", "health_satisfaction",
  "tenure", "net_income", "work_time_weekly", "total_years_unemployment",
  "worr_job_dummy", "worr_financial_dummy", "worr_economic_dummy",
  "male", "age",  "worr_health_dummy", 
  "married_dummy", "university_dummy", "self_employed_dummy", "white_collar_dummy"
)

# Apply pre-processing (center and scale) only to the selected numerical columns
preProcValues <- preProcess(balanced_data[, numerical_vars], method = c("center", "scale"))

# Standardize the training data
balanced_data[, numerical_vars] <- predict(preProcValues, balanced_data[, numerical_vars])

# Standardize the test data
testData[, numerical_vars] <- predict(preProcValues, testData[, numerical_vars])

# Convert `health_decline_2yrs` to factor
balanced_data$health_decline_2yrs <- factor(balanced_data$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))
testData$health_decline_2yrs <- factor(testData$health_decline_2yrs, levels = c(0, 1), labels = c("No", "Yes"))


# Set up the training control
train_control <- trainControl(method = "cv", number = 10, classProbs = TRUE, summaryFunction = twoClassSummary)

# Train the LASSO model for classification using the balanced dataset
set.seed(12345)
lasso_model_balanced <- train(
  health_decline_2yrs ~ .,  
  data = balanced_data,
  method = "glmnet",        # Specify LASSO
  family = "binomial",      # Classification for binary outcome
  trControl = train_control,  # Use predefined training control
  tuneGrid = expand.grid(alpha = 1, lambda = seq(0.001, 0.5, by = 0.001)), # LASSO tuning grid
  metric = "ROC"  # Use ROC as the evaluation metric
)

# Display the best lambda value and model summary
print(lasso_model_balanced$bestTune)

##   alpha lambda
## 1     1  0.001

# Extract the cross-validation results
cv_results <- lasso_model_balanced$results

# Create a ggplot visualization for Cross-validation
ggplot(cv_results, aes(x = log(lambda), y = ROC, color = ROC)) +
  geom_point(size = 2, alpha = 0.8) +  # Add points for each lambda value
  geom_line(size = 1) +  # Add a line to connect points
  labs(
    title = "LASSO Balanced Model Cross-Validation Results",
    subtitle = "ROC vs. Log(Lambda) Across Cross-Validation Folds",
    x = "Log(Lambda)",
    y = "ROC"
  ) +
  scale_color_gradient(low = "#A6CEE3", high = "#1E2B4F") +  # Gradient from light blue to dark blue
  theme_minimal(base_size = 14) +
  theme(
    panel.background = element_rect(fill = "white", color = NA),  
    plot.background = element_rect(fill = "white", color = NA),  

    panel.grid.major = element_blank(),  
    panel.grid.minor = element_blank(),  

    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  
    axis.text.y = element_text(size = 12, color = "#1E2B4F"),  
    axis.title.x = element_text(size = 14, face = "bold", color = "#1E2B4F"),  
    axis.title.y = element_text(size = 14, face = "bold", color = "#1E2B4F"),  

    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  
    plot.subtitle = element_text(size = 14, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  

    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20),  
    legend.position = "none" 
  )

# Save Graph
ggsave("lasso_model_classification_balanced_no_health.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

# Model Evaluation on Original Test Set
lasso_predictions_balanced <- predict(lasso_model_balanced, newdata = testData, type = "prob")

# Predict binary outcomes (threshold = 0.5)
predicted_classes <- ifelse(lasso_predictions_balanced[, "Yes"] > 0.5, "Yes", "No")

# Confusion matrix
conf_matrix <- confusionMatrix(factor(predicted_classes, levels = c("No", "Yes")), 
                               factor(testData$health_decline_2yrs, levels = c("No", "Yes")))
print(conf_matrix)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   No  Yes
##        No  8762 2163
##        Yes 8084 3288
##                                          
##                Accuracy : 0.5404         
##                  95% CI : (0.5339, 0.547)
##     No Information Rate : 0.7555         
##     P-Value [Acc > NIR] : 1              
##                                          
##                   Kappa : 0.0902         
##                                          
##  Mcnemar's Test P-Value : <2e-16         
##                                          
##             Sensitivity : 0.5201         
##             Specificity : 0.6032         
##          Pos Pred Value : 0.8020         
##          Neg Pred Value : 0.2891         
##              Prevalence : 0.7555         
##          Detection Rate : 0.3930         
##    Detection Prevalence : 0.4900         
##       Balanced Accuracy : 0.5617         
##                                          
##        'Positive' Class : No             
##

# Evaluate model performance
print(paste0("Accuracy: ", conf_matrix$overall["Accuracy"]))

## [1] "Accuracy: 0.540431448176885"

print(paste0("Sensitivity: ", conf_matrix$byClass["Sensitivity"]))

## [1] "Sensitivity: 0.520123471447228"

print(paste0("Specificity: ", conf_matrix$byClass["Specificity"]))

## [1] "Specificity: 0.603192074848652"

Excluding health, the performance significantly declines. The accuracy drops from 67% to 54%, the sensitivity also drops from 66.67% to 52% and the specificity from 67.7% to 60%. This means that self-reported health or objective health status strongly correlates with future health decline.

# Convert sparse matrix to data frame and filter non-zero coefficients
coefficients <- coef(lasso_model_balanced$finalModel, s = lasso_model_balanced$bestTune$lambda)

non_zero_coefficients <- data.frame(
  Variable = rownames(as.matrix(coefficients)),
  Coefficient = as.numeric(as.matrix(coefficients))
) %>%
  filter(Coefficient != 0)  # Keep only non-zero coefficients

# Remove the intercept and rename variables
non_zero_coefficients <- non_zero_coefficients %>%
  filter(Variable != "(Intercept)") %>%  # Remove the intercept
  mutate(
    Variable = case_when(  # Rename variables for cleaner labels
      Variable == "health" ~ "Health",
      Variable == "health_satisfaction" ~ "Health Satisfaction",
      Variable == "life_satisfaction" ~ "Life Satisfaction",
      Variable == "educ" ~ "Education Level",
      Variable == "male" ~ "Gender (Male=1)",
      Variable == "worr_job_dummy" ~ "Job Worries (Dummy)",
      Variable == "tenure" ~ "Tenure",
      Variable == "work_time_weekly" ~ "Work Time Weekly",
      Variable == "net_income" ~ "Net Income",
      Variable == "total_years_unemployment" ~ "Total Years Unemployed",
      Variable == "worr_financial_dummy" ~ "Financial Worries (Dummy)",
      Variable == "smoking_dummy" ~ "Smoking (Dummy)",
      Variable == "worr_health_dummy" ~ "Worries About Health (Dummy)",
      Variable == "worr_economic_dummy" ~ "Worries About the Economy (Dummy)",
      Variable == "BMI" ~ "BMI",
      Variable == "age" ~ "Age",
      Variable == "university_dummy" ~ "University (Dummy)",
      Variable == "married_dummy" ~ "Married (Dummy)",
      Variable == "white_collar_dummy" ~ "White Collar Job (Dummy)",
      Variable == "self_employed_dummy" ~ "Self Employed (Dummy)",
      TRUE ~ Variable 
    )
  )

# Plotting non-zero coefficients with cleaner labels
ggplot(non_zero_coefficients, aes(x = reorder(Variable, Coefficient), y = Coefficient, fill = Coefficient > 0)) +
  geom_bar(stat = "identity", color = "black") +
  coord_flip() +  # Flip coordinates for better readability
  labs(
    title = "Non-Zero Coefficients from Lasso Balanced",
    x = "",
    y = "Coefficient Value"
  ) +
  scale_fill_manual(
    values = c("#FF0000", "#1E2B4F"),  # Red for negative, dark blue for positive
    guide = "none"  # Remove the legend
  ) +
  theme_minimal(base_size = 14) +
  theme(
    # Backgrounds
    panel.background = element_rect(fill = "white", color = NA),  # White background
    plot.background = element_rect(fill = "white", color = NA),  # White outer background

    # Gridlines
    panel.grid.major = element_blank(),  # Remove major grid lines
    panel.grid.minor = element_blank(),  # Remove minor grid lines

    # Axis styling
    axis.title.x = element_blank(),  # Remove x-axis title
    axis.title.y = element_blank(),  # Remove y-axis title
    axis.text.x = element_text(size = 12, color = "#1E2B4F"),  # Dark blue x-axis text
    axis.text.y = element_text(size = 12, face = "bold", color = "#1E2B4F"),  # Bold and dark blue y-axis text

    # Title styling
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#1E2B4F", margin = ggplot2::margin(b = 10)),  # Centered and bold title
    
    # Adjust overall plot margins
    plot.margin = ggplot2::margin(t = 20, r = 100, b = 20, l = 20)  # Add more space around the plot
  )

#Save Graph
ggsave("lasso_coefficients_classification_balanced_no_health.png", plot = last_plot(), width = 16, height = 8, dpi = 300)

And similar to previous unbalanced lasso excluding health, the most important predictors are health satisfaction, BMI, Smoking, Age, not having a university degree, not being married, worrying about health, and being a female.

Conclusion

Our study investigates factors that are associated with the decline of individuals’ self-assessed health. Using G-SOEP and applying Lasso Regression and Random Forest, we found good classification performance. Important predictors ranged from current health over personal characteristics to job characteristics suggesting that a holistic view of health is necessary when confronting the issue of health decline.

SOEP Data Preparation

Salma-Anastasiia-Suzanna

2025-02-01

Introduction

1. Setup

1.1 Load Required Packages

1.2 Load the pl Dataset

1.3 Merge with Other Datasets

1.4 Main filtering: Analysis post 1999

2. Outcome Variables: Subjective Health

2.1 Health

2.2 Worries About Health

2.3 Health Trends

3. Predictors

3.2 Life Satisfaction and Health Satisfaction

3.2.2 Height, Weight, BMI

3.2.3 Smoking

3.2.4 Diet

4. Control Variables

4.1 Worries about job security, financial situation, and economic situation

Descriptive Statistics

4.2 Tenure

4.3 Net Income and Working time per week

4.4 Unemployment

4.5 Occupational Status

4.6 Gender

4.7 Migration Background

4.8 Marital Status

4.9 Age

4.10 Education

Final Cleanup: Keeping relevant & cleaned variables

Saving the cleaned dataset

Investigating the dataset

Correlation Heatmap

Gender Disparities

Educational Level Disparities

Income Level Disparities

Box Plot of Net Income by Education Level

Age Disparities

Scatter Plot of Net Income vs. Age

Marital Status Disparities

Box Plot of Age by Relationship Status

Disparities by Place of Birth

Relationship between subjective and objective health

Prep for Analysis

Create new dummys

Visualise new dummies

Summary Statistics

Detailed Summary Statistics Tables

Short Summary Statistics Table

Modelling

Lasso Classification: Health worries as an outcome Variable

Evaluating the distribution of our outcome variable: Health in 2 years -categorical-

Lasso Regression: Health in 2 years -categorical- as an outcome Variable

Interpretation

Evaluating the distribution of our next outcome variable: Health decline in 2 years -dummy-

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable, excluding Health in t-1

Random Forest Classification: Health decline in 2 years -dummy- as an outcome Variable

Interpretation

Partial Dependence

Next steps

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable, WITH undersampling

Lasso Classification: Health decline in 2 years -dummy- as an outcome Variable, WITH undersampling, excluding Health in t-1

Conclusion